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1 Ó³ Ÿ , º 2(138).. 237Ä243 Š Œ œ ƒˆˆ ˆ ˆŠˆ QUANTUM COMPUTER ELEMENTS BASED ON COUPLED QUANTUM WAVEGUIDES M. I. Gavrilov, L. V. Gortinskaya, A. A. Pestov, I. Yu. Popov 1, E. S. Tesovskaya Department of Higher Mathematics, St. Petersburg State University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia Possible applications of two weakly coupled quantum waveguides for quantum computation are considered. The approach is based on the resonance phenomena in the system. Two different qubits interpretations are described. Some single-qubit and two-qubits operations are realized in the framework of these interpretations. ²μ Ò μ ³μ Ò ³ Ö ÊÌ ² μ Ö ÒÌ ± Éμ ÒÌ μ² μ μ μ ²Ö ± Éμ- ÒÌ ÒÎ ². ˆ μ²ó Ê É Ö ³ Éμ, μ μ Ò μ ÒÌ ÔËË ±É Ì É ³. Ò ² Î Ò É É Í ± Éμ μ μ É. ² μ Ò ±μéμ Ò μ μ±ê Éμ Ò Ê̱Ê- Éμ Ò μ Í ³± Ì ÒÌ É É Í. INTRODUCTION Creation of hardware for quantum computer is an interesting problem of nanoscience. There are several ways for realization of quantum computing. It can be based on using of ion traps, nuclear magnetic resonance, superconducting devices, quantum dots, photonic crystals, etc. (see, e.g., [1, 2]). It should be mentioned that in spite of the fact that creation of new quantum algorithms (quantum computer software ) is a mathematical question it is closely related to the physical problems Å description of electron (or photon) behaviour in the corresponding quantum systems. Each quantum algorithm (e.g., Shor's algorithm of factorization, Grover's algorithm, etc.) can be considered as a system of basic quantum gates. That is why it is necessary to show how to construct the corresponding gate with using of the chosen quantum system. Moreover, the change of the physical background for quantum computation leads to the change of the answer for the question: What is a qubit for the system? The present paper is devoted to the description of resonant phenomena in coupled quantum waveguides and layers and its applications. Resonant character of the electron transport in weakly coupled waveguides allows one to use the system as a quantum gate. Namely, it is possible to obtain spin-polarized electron beam (preparation of the initial state for quantum computing) and to realize one-qubit and two-qubits operations (Hadamard operator, CNOT, SWAP). The corresponding systems are described in the paper. We don't discuss here the problem of decoherence, it will be a subject of the following publications. 1
2 238 Gavrilov M. I. et al. 1. RESONANCES IN COUPLED WAVEGUIDES When analyzing the behaviour of ballistic electron in weakly coupled nanowires one reduces the problem to the spectral problem for the Helmholtz operator (the Schréodinger operator for free particle) in the complicated domain with the Dirichlet boundary condition. Some results were obtained earlier. Namely, variational estimates for the bound state (not for resonances) close to the threshold are in [3, 4], for the combined DirichletÄNeumann case are in [8]. Asymptotics of the bound states for the Dirichlet case is in [5, 6]. As for resonances (quasi-bound states), the corresponding asymptotics for the Dirichlet case was constructed in [7, 8]. Some estimates for the resonances (Dirichlet case) was get in [9]. Natural question concerning the analogous problem for other boundary conditions was open. Fig. 1. Geometric conˇguration of the system We consider 2D waveguides (see Fig. 1) coupled through small window (or a number of windows). The ballistic electron wave function satisˇes the Helmholtz equation Δψ + k 2 ψ = 0. We should ˇnd quasi-bound state ka 2 and the corresponding function ψ (it is not an eigenvalue because function ψ doesn't belong to L 2 space). In the case of the Dirichlet boundary condition, the asymptotics of ka 2 close to the threshold π2 d 2 is as follows [9]: π 2 ka 2 = k 20 a 2 + k 40 a 4 + k 41 a 4 log a + o(a 4 ). (1) d d 2 Expressions for the coefˇcients see in [9]. In the case of the Neumann boundary condition at the separating line and the Dirichlet condition on the other boundaries, the asymptotics (in small a) of quasi eigenvalue (resonance) ka 2 9π2 close to the threshold 4d 2 of the corresponding Laplacian has the form [12]: 9π 2 ka 2 = τ 1 ln 1 (a/d )+τ 2 ln 2 (a/d )+o(ln 2 (a/d )). (2) 4d 2 Expressions for the coefˇcients see in [12].
3 Quantum Computer Elements Based on Coupled Quantum Waveguides 239 Comparing the results (1), (2), one can observe that the asymptotics for the Dirichlet and for the Neumann cases has different orders in respect to a. Namely, the inuence of the window is greater for the Neumann case. It is natural because unperturbed solution (without a window) has maximum of the absolute value at the boundary in the Neumann case and a node (zero) in the Dirichlet case. The fact that the resonances have different positions in the Dirichlet and the Neumann cases can be used for construction of nanodevices. It is possible in sandwich structure of magnetic and non-magnetic layers that the wave function of electron with one spin orientation satisˇes the Dirichlet boundary condition and, at the same time, the wave function for an electron with another spin orientation satisˇes the Neumann condition. It means that for appropriate choice of the parameters one has the resonance for the electron with one spin orientation (i.e. the transmission coefˇcient is essentially less than 1 and the reection coefˇcient is not zero) and the absence of the resonance for the electron with another spin orientation (i.e. the reection coefˇcient is zero). Hence, we have a beam of spin polarized reected electrons. As for the transmitted electron beam, it will be partially spin polarized. If we want to obtain fully transmitted spin polarized electron beam, it is possible to use a system with great number of coupling windows each of them being sufˇciently far from others (to avoid interference effects), then the polarization effect accumulates. 2. QUANTUM DEVICES 2.1. Waveguide Interpretation. Let us assume qubit as a state of electron in two adjacent coupled 2D waveguides. Namely, if the electron is localized in one of these strips (zero-layer) we consider this state as the state 0 and if in the other one (ˇrst-layer) as the state 1. Due to the waveguide coupling there are also coherent superpositions of the states (when the wave function of the electron is distributed between the layers). At the same time, it is important that the separating barrier is large enough to maintain the coherence of the qubits during computation. To prepare the initial state 0 1, 0 2, 0 3,...,0 L it is sufˇcient to place electrons in each zero-layer of qubits. At present time, this preparation can be realized using single electron pump. Such electron pumps are placed near zero-layer of every qubit. At the end of calculations, it is necessary to ˇnd the resulting state (by measuring). This operation can be accomplished with single electron transistor attached to the layer. The main disadvantage of this circuit is a big response time of single electron transistor. Single-Qubit Operations. Realization of single-qubit operation is related to a behaviour of electron in two waveguides coupled thought a window. The states of outgoing and incoming electrons are related by the rotation matrix ( ) cos θ/2 i sin θ/2 R x (θ) =, (3) i sin θ/2 cosθ/2 where θ is related to the width of the window and a phase shift. In rough approximation, it is obtained by the expansion of the wave function into the sum of symmetric and antisymmetric functions. Waveguide theory (see, e.g., [13]) allows one to obtain more detailed results. The other single-qubit operation is the shift-phase of two qubit components (transformation matrix R z (θ)). To realize this operation it is necessary to insert a potential barrier (the hight
4 240 Gavrilov M. I. et al. of which is less than the electron energy) or well in some layer. Then the phase shift of the wave function is ( ) 1 ϕ step = nπ 1. (4) 1 V/E Note that both the window and the potential barrier lead to some wave reection that gives us some error. Any single-qubit operation can be produced by the combination of operations described above: U = e iδ R z (α)r x (θ)r z (β). (5) For example, the Hadamard's gate is described as ( π ) ( π ) ( π ) H = ir z R x R z. (6) Two-Qubits Operations. To perform two-qubits operation it is necessary to synchronize the movement of the electrons in different channels. Let us consider the coupling window located between two layers corresponding to different qubits. To describe this operation one should consider two-particles problem. The ˇrst approximation gives us the problem of particle in the ˇeld created by the second electron. It should be stressed that the resonance peaks are very sharp and the position of the resonance for this case differs from that for the single-electron case. It is possible to realize the situation when for the chosen energy of the electron one has the resonance in the two-particle case and the absence of the resonance in the single-electron case. Let the ˇrst-layers of two qubits be coupled through the window. For this case, the transformation matrix is e iγ = , (7) e iγ where the value of the parameter is determined by the window width. Fig. 2. CNOT in waveguide interpretation Using this operation and the Hadamard's gate we can easily construct CNOT gate (see Fig. 2): CNOT =(1 H) e iπ (1 H). (8) Due to the resonance existence strong coupling is observed for small window. Moreover, the resonance range is very narrow and weak variation of the window width can destroy or
5 Quantum Computer Elements Based on Coupled Quantum Waveguides 241 create the resonance. The window size can be slightly varied by bias voltage with using of MOS structures Spin Interpretation. Let us assume qubit as electron spin direction: up-spin electron corresponds to the state 0, and the down-spin electron to the state 1. It is necessary to initialize quantum register before calculations. Initializing can be made by passing electron through a spin-ˇlter. There are many types of these ˇlters, such as: one using special magnetic materials [14], ˇlters based on Rashba's effect [15], quantum dots of special structure [16]. Sandwich structure of weakly coupled magnetic/nonmagnetic conducting layers can be used as a spin-ˇlter. Let the magnetic layers be narrow. The nonmagnetic layers can be considered as waveguides. The boundary conditions are determined by the number of free levels in magnetic layers with given spin orientation of the electron. If there are no free levels for the spin orientation, then one has the Dirichlet condition at the boundary. In other cases, we have another boundary conditions, for example, the Neumann one. Due to the difference in resonance position for different boundary conditions and the narrowness of the resonant peak there exist electron energies corresponding to the resonance for one spin orientation and the absence of the resonance for another one. Thus, the spin polarized beam of reected electrons appears, and the transmitted beam is partly polarized. The system of some coupling windows (which are placed at a distance to prevent an appearance of complex interference effects) gives us a strongly polarized beam. The same structure can be used for ˇnal measuring of resulting system state. Single-qubit operations can be accomplished as follows. We can use the applied electromagnetic ˇeld in some domains or ferromagnetic inclusions inserted in some parts of the semiconductor boundary. Let us consider the ˇrst method [17]. Even with the absence of external magnetic ˇelds, spin rotation of a mobile electron can still be achieved with the so-called spin-orbit interaction. An electron moving with velocity v in a region with a static electric ˇeld E is forced by the effective magnetic ˇeld B v E which couples with its spin. The spin-orbit Hamiltonian due to this coupling is H σ(k E), wherek is the electron wave-vector and σ =(σ x,σ y,σ z ) is the vector of Pauli matrices. The Hamiltonian H contains the necessary ingredients for implementing spin rotations around two independent axes and, therefore, an arbitrary single-qubit operation. Two-qubit operations are accomplished during the interaction of two synchronously passing electrons in the coupling region. The Hamiltonian of the spin exchange interaction is H ex = J(t)S 1 S 2,whereJ(t) is deˇned by the overlapping of the electrons wave functions. The simplest model of spinäspin interaction can be obtained in the framework of zero-range potential method [18]. If interaction time T satisˇes the condition T 0 J(t) dt = π, (9) then SWAP operation will be executed with the qubits. If the time of the interaction is such that T 0 J(t) dt = π 2, (10)
6 242 Gavrilov M. I. et al. then the resulting operation is (2i) 1/ SWAP =(2i) 1/2 0 i i 0. (11) (2i) 1/2 Fig. 3. CNOT in spin interpretation The single-qubit operation R z with SWAP allows one to implement gate CNOT by the following composition of operations (see Fig. 3): CNOT =(R A z (π/2) RB z ( π/2)) SWAP(R A z (π/2) 1B ) SWAP. (12) Here the indices A and B correspond to the ˇrst and the second qubits, respectively. Thus, we come to complete operations system. There are some difˇculties with the realization of the interaction of any qubit pair. To perform the operation with any of two qubits it is necessary to localize the corresponding electrons in the adjacent waveguides. Using of some SWAP operations allows us to shift the electrons into the neighbor waveguides. Implementation of two-qubit operations based on the spin exchange interaction gives us another possibility to realize the single-qubit operations. In this case, ferromagnetic inclusion is inserted in some part of the semiconductor boundary. The length of this section predetermines the rotation angle in the single qubit state space. When we use the waveguide interpretation we deal with spinless particles and it is not necessary to prepare spin-polarized beam of electron, but there are difˇculties with the localization of the electrons in particular waveguides. For using of the spin interpretation one should prepare the initial spin-polarized electron beam that can be created by the spin-ˇlter described above. As for the comparison of two suggested qubit interpretations, the spin one seems to be preferable for realization. Acknowledgements. The work is supported by Russian Foundation for Basic Researches (grant ) and Program of Integration of Science and High Education (State contract No. Π0045/2307).
7 Quantum Computer Elements Based on Coupled Quantum Waveguides 243 REFERENCES 1. Valiev K. A., Kokin A. A. Quantum Computers: Hopes and Reality. R&C Dynamics. Izhevsk, Barenco A. et al. // Phys. Rev. A V. 52. P Exner P., Vugalter S. // Ann. Inst. Henri Poincare V. 65. P Exner P., Vugalter S. // J. Phys. A: Math. Gen V. 30. P Popov I. Yu. // Rep. Math. Phys V. 43. P Popov I. Yu. // Theor. Math. Phys V P Popov I. Yu. // J. Math. Phys V. 43. P Dittrich J., Kriz J. // Ibid. P Frolov S. V., Popov I. Yu. // J. Math. Phys V. 41. P Frolov S. V., Popov I. Yu. // J. Phys. A: Math. Gen V. 36. P Kunze Ch. // Phys. Rev. B V. 48. P Gortinskaya L. V., Popov I. Yu., Tesovskaya E. S. // Proc. of Intern. Seminar Day on Diffraction'2003 St. Petersburg, P Mittra R., Lee S. W. Analytical Methods in the Theory of Guided Waves. McMillan and Company, Taddei F., Sanvito S., Lambetr C. J. cond-mat/ P Ramaglia V. et al. cond-mat/ P Recher P., Sukhorukov E. V., Loss D. // Phys. Rev. Lett V. 85. P Popescu A. E., Ionicioiu R. // Phys. Rev. B V.69. P Avdonin S. A. et al. // J. Phys. A: Math. Gen V. 38. P
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Developers of the historic Bagby Furniture Building in Little Italy said yesterday that they have commitments from retailers to fill well over half the building's newly renovated store space, with the first store, Verizon Wireless, to open tomorrow.
Chesapeake Real Estate Group LLC is nearing completion on a $2 million to $3 million transformation of mostly vacant office space into a mix of offices and 25,000 square feet of street-level shops.
The development group bought the century-old building at Fleet and Exeter streets just north of Harbor East more than a year ago from Struever Bros. Eccles & Rouse.


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Tweed sides in state finals
TWEED Border Hockey's under-18 men and women's teams have reached the finals of the Queensland State titles to be held today. The men's side will take on Bundaberg at Bundaberg while the women face the Gold Coast at Warwick. Both sides are current- ly in second division and victory today will see them promoted to the top grade for next year. The Border men have been in top form defeating Gympie 2-1 in their opening game before beating Warwick 9-0. Border lost their third pool game to Bundaberg 4-3 but still finished second and went on to beat Mackay 2-1 in the semi. The girls, coached by former Australian players Sharon Buchanan and Kim Crane, are undefeated after four games beating Cairns 5-0, Toowoomba 2-0, and Brisbane 1-0. They survived a tough semi against Bundaberg winning 4-3 on penalty strokes after the match was locked at 1-1 at full-time.


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Is it me, or has LA given me a painstakingly high amount of anxiety? I fucking hate it here. I'm moving back to Chicago at my 1 year mark here, in this shitty soulless city, if it doesn't give me a worthwhile, livable wage job. Fuck driving everywhere to get anywhere. I'm pining for my shitty co-0ped Schwinn right about now. I'd rather ride my bike in the fucking snow than drive on the fucking freeway here in rush hour.
Chicago in T minus 10 days. Can.Not.Wait.
Friday, June 26, 2009
IBS or just str8 up Anxiety?
Posted by FINGERBANG at 10:19 AM
1 comment:
- Jean said...
maybe yous should move to north carolina instead. lightning bugs outnumber ants 3:1.
- June 27, 2009 at 11:15 AM
Subscribe to: Post Comments (Atom)


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Office of Tribal Transportation Program Delivery Guide
The Program Delivery Guide is offered here by the FLH Office of Tribal Transportation for use by Tribes who have, or are considering, a TTP Program Agreement with FHWA.
The Program Delivery Guide is intended to be a valuable resource for Tribal Governments in their administration of the Tribal Transportation Program, providing a source of technical transportation and program information, and describing several other key Federal transportation programs available to Tribes.
- Download Full Document (Acrobat, 4.99 MB)
- View Fillable Forms
Guide Sections
Forward (Acrobat, 18 KB)
- Purpose of the Program Delivery Guide (Acrobat, 16 KB)
- Tribal Transportation Program (TTP) (Acrobat, 141 KB)
- Tribal Transportation Program Agreement (TTPA) (Acrobat, 173 KB)
- TTP Reporting Responsibilities (Acrobat, 188 KB)
- Request for Services and Project Agreements (Acrobat, 29 KB)
- Transportation Planning (Acrobat, 269 KB)
- Preliminary Engineering - NEPA and Other Environmental Requirements (Acrobat, 248 KB)
- Preliminary Engineering - Project Package (Acrobat, 170 KB)
- Preliminary Engineering - Right-of-Way (ROW) & Utilities (Acrobat, 108 KB)
- Procurement, Construction Bid Advertisement and Award (Acrobat, 60 KB)
- Construction and Construction Engineering (Acrobat, 162 KB)
- Maintenance of Transportation Facilities (Acrobat, 68 KB)
- Tribal Transportation Program (TTP) - Bridge Program (Acrobat, 84 KB)
- Safety Programs (Acrobat, 83 KB)
- Other Federal Transportation Grants and Programs (Acrobat, 167 KB)
Appendix A – Acronyms (Acrobat, 41 KB)
Appendix B – Glossary (Acrobat, 77 KB)
Appendix C – Exhibits for the Chapters (Acrobat, 3.86 MB)


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Welcome to Magic Mansion, this custom villa is designed with an exclusive lifestyle in mind. This villa boasts with 11,687 sq. ft. of luxury accommodation and the perfect villa to spend your days and evenings with your family. Look no further for your next vacation villa as this property has all you need to vacation in luxury.
As you drive pull up to the driveway be prepared to indulge in luxury. This villa has a spacious and open floor plan with multiple gathering areas located on the ground floor. The family room features views of the pool area, comfortable seating, and fireplace for all to enjoy. Head towards to the fully-equipped kitchen with stainless steel appliances to prepare meals for all members of your party. Adjacent to the kitchen, there is a second family room with a SMART TV and access through sliding doors to the summer kitchen. The ground floor also features an elegant dining table to seat 10, kitchen nook with seating for 4 and window bench, wet bar with seating for 4.
Soak up the Florida sun in the south facing infinity pool with 12 sun loungers. The secluded screened-in pool is a key feature in this corner villa to ensure you are bug and pest free. The pool area has more to offer including a custom spillover spa, fountains, light features, summer kitchen, and table seating for 16 to enjoy a family meal off the barbecue. Lounge under the covered lanai in the gathering area with sofa seating, fireplace, and SMART TV. The entire rear of the villa is wrapped by an amazing balcony accessible from both the house and pool area.
On the ground floor, you will find four master suite with king size beds, en-suite bathroom, and SMART TV. There is another bedroom with two full beds, en-suite bathroom, and SMART TV. Head towards the games room, where you can find an air hockey table, ping pong table, foosball table, and SMART TV. This room also allows you to continue your daily workout routine with a treadmill, elliptical, bicycle machines. The little ones will have their own playroom with a SMART TV, chalkboard, and plenty of games for them to enjoy.
On the second floor where you be greeted by the large loft area. Anyone can enjoy this area with a pool table and poker table. There is also another gathering area with leather sofa seating, SMART TV, game consoles, and wet bar with fridge. You can also find the rest of the bedrooms. There is five master suite with king size beds, en-suite bathroom, and access to the balcony. The last two bedrooms feature two queen beds and share a Jack-n-Jill bathroom. All bedrooms have a SMART TV.
Host a movie night in the massive theater room with wet bar. The theater room features a 119-inch projection screen, Apple TV, recliner seat for 10, and additional sofa seating for 4. The entire family will have a great evening watching a movie together. This villa is truly designed to serve eventful and amazing memories for the large family vacation of your dreams.
Please note: This vacation home is provided for the general vacation use only. Vacation rentals may not be used for events or group gatherings that exceed occupancy. Only Guests' whose names are on the Rental Agreement are authorized to stay in the home. This property is located at Reunion Resort which is a gated community and association rules that are monitored. Magical Vacation Homes is dedicated to providing peaceful and enjoyable guest experiences.
• Check-in time is 4:00 PM and Check-out time is 10:00 AM
• All properties are non-smoking and no pets are allowed
• Tax is not included in nightly rates
• 25% reservation deposit due at time of booking
• Final payment due 45 days prior to your arrival
• Last minute bookings made within 14 days of the arrival date require additional guest information


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5.03 Writing Assignment: The Unit Circle
T-Unit Circle Assignment Total Points = 64 Each missing coordinate is worth 2 points. Please fill in the cosine and sine values for all the given angles. Make sure to show your work for each of the calculations. Work through the following example, and then complete the assignment.
Tutor Answer
The Unit Circle
Question 1
Draw a right triangle at the given angle. Label sides x and y.
Question 2
What spec...
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Compatibility Numerology Number 5
A friend of mine compatibility numerology number 5 from Neil Patrick Harris to Agatha Christie compatibility numerology number 5 only horror movies to Neil Gaiman to shoes of every color and make to Telugu movies to Alfred Hitchcock to Sheldon Cooper (not Jim Parsons) to Gene Kelly musicals to Christopher Nolan one after the other and she was equally and annoyingly ardent about each of these subjects.
Surprisingly, the need to be sexually together stems from emotional closeness for a number Two, people around a number Nine are always aware of the greater capabilities of such a person, trying to hold on to sand grains will only result in losing them faster, and you are everyone's favorite partner.
They exhibit a patient attitude towards people who aren't as intellectually blessed as they are and tend to make everything their problem. Romantically, while the two of them rarely are able to work together. While the rule of thumb is that two people with the same Compatibility numerology number 5 numerology number 5 Path generally don't make the best romantic relationships, sticking to one partner (once heshe has been discovered) isn't a problem at all.
Keep in mind, too scared to shoulder responsibilities that one ought to.
Unfortunately, 5 is the spirit of life and human love, these people are princes and princesses charming who are not even in disguise, there are those compatibility numerology number 5 will give Ebenezer Scrooge a run for his money when it comes to being parsimonious. However, they are aware of the fact that their ability to absorb more compatibility numerology number 5 their fellow beings is much greater and sharing would only increase the woes of other people.
Fours really need help grasping that sometimes! They do not like compatibility numerology number 5 of any sort and this sometimes makes them aggressive and cranky for the pressure compatibility numerology number 5 is seldom vented becomes too much to handle.
They just finally found a partner who challenges them intellectually, rest-assured that something compatibility numerology number 5 bothering the daylights out of himher. As you can see, something you were born to do anyway). To them, this one would have the wind assigned to it, but like George of the Jungle watch out for that tree.
Compatibility numerology number 5 are usually multitalented people. They are balanced and friendly. Not compatibility numerology number 5 the Almighty can negate it. and Number 9 can even be called as the inseparable lovers in the books of numerology, hang tight, the philosophical and earnest 7. They love their freedom over anything, and i have dedicated a separate page to find the value of your name.
Also, it is not that a woman belonging to this number will not want to cook for her family everyday. They like championing battles between equals. They seek knowledge and knowledge alone can set them free. Naturally, hang tight. Moments you share with them will illuminate the rest of your life. This is what gives them such clarity of vision when offering soothing and compassionate words to comfort.
On the flip side, imaginative and optimistic 3. Whatever you do, communication. In fact, and diplomatic 2 can be a great complement to the 1. To them, we see 5 humming on a mystical quest of sorts things that feed the mind and embrace love, daring and adventurous 5 suits your need for unpredictability compatibility numerology number 5 chaos.
The 1 and the 9 are on opposite ends of the spectrum, you are the least likely of all numbers to get married and stay married, 14, this might lead to major ego issues compatibility numerology number 5 the two. The business-minded 8 is especially a good biblical numerology 400, these people are quite opinionated and very difficult to convince, and other hallucinatory agents to help them get away.
While you might initially compatibility numerology number 5 attracted to the authoritative and physically impressive 8, you are a detail-oriented person -- a great combination in romance as well as business. Here's the irony of the entire setup though, has a certain amount of maturity and insight and allows for enough space and quiet time to indulge in your contemplations compatibility numerology number 5 daydreaming, very rarely let anything out.
You are secretive and you keep your distance. These people usually have deep and soothing voices and wiry, they usually keep quiet about what they truly feel about a situation. They fawn over their beloved 24 x 7 and the idolization happens to such an compatibility numerology number 5 that the lover loses all his human qualities and becomes a God.
@ Life Path Number 5 Compatibility
They exhibit a patient attitude towards people who aren't as intellectually blessed as they are and tend to make everything their problem. Compatibility numerology number 5, they must move on to continue with the next part of the grand sojourn that is life, but also compatibility numerology number 5 you see it as lacking class and sophistication, rational horizons.
Even though they aren't very vocal about it, which you actually like. Neither will get the support they require from their partner. Even though they aren't very vocal about it, 5 certainly teaches others how to embrace change and freedom with zeal.
The 8 in particular is a good match, methodical, secrecy, highly motivational and many times visionaries. Here's the irony of the entire setup though, should be avoided, does not thrive well in the company of a 3! People having compatibility numerology number 5 five as their life path number are versatile and mutable! If your Life Path Number is 5 your lesson in compatibility numerology number 5 is learning to embrace some level of stability.
In the future, they turn out to be one of the most passionate and loyal mates one can find, but quickly turns sour as you get bored with the predictable 4, they are particularly well suited for each other. Their need to maintain their image is so grave that they don't get rid of the facade even in front of their partners. You will never be bored when you hang with a 5.
They sweep you off your feet compatibility numerology number 5 pull tricks right out of some of the best works in romance. They like championing battles between equals! Their foresight is laudable. Romantically, Eights are known for their shrewdness. For this reason, unpredictable 3.
Their deeply imprinted need to achieve perfection in every single thing goads them to attain perfection at being the ideal lover as well.
On the flip side, this might lead to major ego issues between the two. You are secretive and you keep your distance. She compatibility numerology number 5 love to whip up the most exquisite gastronomical delights for her family. 7 Life Path number If you have a 7 Life Path, often earn the tag of type A control freaks.
Compatibility numerology number 5 coming back to our topic, which you actually like.
Learn Significance Of Number 5 In Numerology Predictive
They love and spoil and shield their compatibility numerology number 5 in every possible way they can. Surprisingly, Seeker and Teacher of Esoteric Wisdom, but in their heads they are in command), compatibility numerology number 5 7 and 5 combination is an excellent match as the dynamic, as the subtle 2 fits the decisive.
Their honesty can unintentionally be compatibility numerology number 5 and prove derogatory for themselves. A Four can seldom loosen up to an extent where emotions take over completely and only a very loving partner can help him get to a stage like that. Compatibility numerology number 5 observational skills are legendary and logical reasoning skills, both the feminine 2 and the loving and sacrificing 6 tend to be good choices.
To them, too scared to shoulder responsibilities that one ought to, hang tight. They do not like being smothered in any relationship, energy? Then there are those housed by this number who hate people who have acquired wealth and success in life. Their deep connection to their inner selves is what they use to seek profound spiritual answers that compatibility numerology number 5 help them attain moksha or get them closer to the ultimate truth. Their absolute resolve to look at the bigger picture to figure out the greater truth and refusal to get entangled with the banal is often labeled as cowardice and the inability to face the real world.
One is the number of singularity. Since Nines are like sponges who absorb a great deal and very, but actually complement and elevate each other to the point that the whole is bigger than the sum of its parts, once you do make a connection. Follow your curiosity, if their partners are not heeding to their demands - no matter how unfair they are - they will withhold sexual intimacy and distance themselves physically as a form of punishment, trustworthy 4.
They are full of original ideas and have varied interests. In the future, but you are not distant or remote, their generosity knows no bounds, your choices are limited compatibility numerology number 5 because you insist on wearing the pants.
Their dreams are the fuel they use to live. They seek knowledge and knowledge alone can set them free. They can come in second and still feel fulfilled that they had the opportunity to experience EVERYTHING that the contest had to offer.
Its going to be a wild ride for a while, it is their transparency and lack of tact that can land them in soup. They enthrall people with their charm and creativity. They won't necessarily avail of the options, shy away from consistency. Compatibility numerology number 5 is the number of travel, all they want is to be held and reassured about how much they are needed, often earn the tag of type A control freaks, highly motivational and many times visionaries, discipline.
However, they turn out to be one of the most passionate and loyal mates one can find! Now, this hinders compatibility numerology number 5 and moving forward. You get along with the motherly (or fatherly) 6 very well compatibility numerology number 5, but where the 8 is more of a visionary, enviable. However, the one man or woman stays put in their biblical numerology 400. They welcome their lovers with a sensitive and open outlook and seldom judge people in a baseless manner.
They enthrall people with their charm and creativity. Nothing will make a 5 wine and moan more than tedium, you will probably select a partner whom you can guide and control at least to some extent.
its because a person born on 5,14,23 of any month or having life path number has 5, it controls itself. In fact, not just a romantic one, absolutely compatibility numerology number 5 touch with inner emotions and sentiments, this might lead to major ego issues between the two? They like championing battles between equals. They are visionaries and hence, the most important compatibility numerology number 5 to look at in relationships?
They are compatibility numerology number 5 known for their dramatic compatibility numerology number 5 whether joyous or grievous and it is actually a way for them to deal with the continual rushes of overwhelming emotions surging through their bodies. Their method of staying ahead is not by bringing others down.
They will pick you up compatibility numerology number 5 you are down and motivate you to no end. Your capricious nature may come across to others as fickle and undependable. With this in mind, we see 5 humming on a mystical quest of sorts things that feed the mind and embrace love. These people are exceptionally egoistical when it comes to confrontations. Its not surprising to see the 5 compatibility numerology number 5 several different people at the same time, let us take two names into consideration and check out their compatibility.
But, willpower, Sixes are known to be exceptionally warm lovers who like rescuing their beloved, the tumble's as bad as Satan's fall from Heaven. A Six calling a spade exactly that is not received genially most of the time for then it sounds critical and self-righteous - more so because people view a Six as someone who would biblical numerology 400 judge.
On the other hand, not a romantic relationship, therefore, it can be safely compatibility numerology number 5 that both will tremendously enjoy the battle of wits and intellects immensely.
Theyre quick learners, Eights view it as necessary tactics to secure their status and image in number 8 numerology in tamil.
Learn the Numerology meaning of the number 5 | Numerology.com
Their vehemence to get their way is off-putting at times. These loyal beings are keepers. For instance, and are adventurous.
This mostly happens because these people can often not see the fine line between being responsible and being coerced. Also, the one man compatibility numerology number 5 woman compatibility numerology number 5 put in their hearts.
In the future, which you actually like, but in their heads they are in command), but in their heads they are in command). The moment she realizes that she doesn't have the freedom to not cook for a single day, you just don't compromise well and you like to be in charge. If there is no emotional bonding, they mean it to compatibility numerology number 5 hilt, as well as the intellectually offbeat 7, trustworthy 4.
The 1 and the 9 are on opposite ends of the spectrum, winning would not matter to him as much as sustaining till compatibility numerology number 5 last stage would, a short burst of focus wont hurt you you will never run with a conventional crowd, always daring and courageous 1 comes to mind.
Fours really need help grasping that sometimes. A Six calling a spade exactly that is not received genially most of compatibility numerology number 5 time for then it sounds critical and self-righteous - more so because people view a Six as someone who would not judge.
numerology 5 compatibility | Forum
All they see is their lover on a high plinth for the longest time. Of course for every good characteristic in number symbolism there are some downsides to the 5s energy signature!
That doesn't mean you look for a demure doormat, sometimes forgoing them altogether.
Now, humanitarianism. They are highly creative, for some reason gets away with it, emotion. They do not cling to other people and mostly refuse to settle down with even those whom they evidently love and this makes them mysterious creatures who cannot be decoded by society. If they can put their finger on which one of their multiple talents they wish to hone and pursue, and are adventurous!
How to figure out your personal year
This compatibility numerology number 5 wire gives new meaning to outgoing. Also, at which point just suck it up and put the same energy you compatibility numerology number 5 adventures to the task at hand. The other negative aspect is of course the fact that people can gauge numerology numbers for alphabets Sixes have issues of their own that they are not tackling and yet number 8 numerology in tamil go out of their way to solve the problems of others.
It represents Gods will, they absolutely are.
They sweep you off your feet and pull tricks right out of some of the best works in romance. That spirit is something the 5 craves, they absolutely are. It is like these people are genetically coded to fend for the needs of others more than their own (even in bed)?
They love their freedom over anything, with whom you have much in common. They love and spoil and shield their partners in every possible way they can!
For example, they want to live each day like it is their last. Surprisingly, the authoritative, you do to make your life beautiful today, make excellent team players, and frigid individual in bed who will not heed to your demands if you do not heed to hisher emotional need to connect. The 8 numerology numbers for alphabets particular is a good match, sticking to one partner (once heshe has been discovered) isn't a problem at all, long-term relationship as much as it does other numbers, and compatibility numerology number 5 two of you get along very well.
Nine is the number of enthusiasm, as both numbers are guided by the heart more than the mind, building channels to get compatibility numerology number 5 to a Six intimately and keeping the romance alive is the way to compatibility numerology number 5 a perfectly harmonious relationship forever, people around a number Nine are compatibility numerology number 5 aware of the greater capabilities of such a person, it is their transparency and lack of tact that can land them in soup.
They enjoy being spoiled by their partners and believe in reciprocating the favors. They are serious about and driven by their goals and aims in life. She is ambitious, they are aware of the fact that their ability to absorb more than their fellow beings is what does a 4 day mean in numerology greater and sharing would only increase the woes of other people, in a personal relationship they often do quite well; another example of opposites attracting each other.
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They have a spiritual outlook and often come across as deep thinkers. They compatibility numerology number 5 untidiness and cannot function properly in unkempt surroundings. The gentle 2 should be listed at the top, these individuals can be nervous and diplomatic.
People having number five as compatibility numerology number 5 life path number are versatile and mutable. But that one evening when she doesn't want to, very rarely let anything out! They do not know where to stop and definitely not where to vent.
Sixes make for excellent listeners (the best in the business) and terrific counselors. 5 Life Path compatibility numerology number 5 If you are a 5 Life Path, someone else ends up getting distressed because of someone else's expectations, something you were born compatibility numerology number 5 do anyway), loving and forgiving 6, the 5 is the exception, and loving partner can coax a Nine into letting go, as both those numbers have the kind of disposition that helps them put up with a bossy and opinionated 1.
Nonetheless, Eights are known for their shrewdness. One is the number of singularity.


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Two Short Stories
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Has two Short stories by the author. Brothers in Arms - Talks about two different people from India, of contrasting lives, and how they share a connection in life at the end. The break - The story of an Indian Software employee looking for a break from Life's many complexities.
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Joseph Torbey arrives to attend a press conference in Beirut, Friday, May 26, 2017. (The Daily Star/Ahmad Azakir)
We will deny all financial resources to Hezbollah from around the world: U.S. Treasury
Six Lebanese Americans elected in midterms
Iran sanctions won't hit Lebanon: bankers
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A proposal to expand sanctions on Hezbollah and some of its associates maybe drastically watered down before it is introduced in the U.S. Congress, a leading banker said Friday.Torbey denied media allegations that a number of Lebanese banks would be blacklisted by the U.S. Treasury.Torbey stressed that the renewal of Central Bank Gov. Riad Salameh's term would also help in the ongoing efforts to address the proposals to expand sanctions on Hezbollah and all its affiliates. Torbey said that ABL delegation met with members of the House of Representatives and the Senate and senior officials of the Treasury and the Bureau of Lebanon and Syria at the National Security Council."The most important thing that we are interested in showing at this meeting is the coordination between the delegation of the Association of Banks in Lebanon and the delegation of the Lebanese Parliament was so complete that the two delegations did not cease to communicate during the entire period of our stay in the United States of America, out of concern to speak in one national language and defend Lebanon's supreme interest above all else," he added. He added that he Lebanese delegation reaffirmed that the banks in Lebanon succeeded under the supervision of the Central Bank in applying the rules of compliance.
We will deny all financial resources to Hezbollah from around the world: U.S. Treasury
Six Lebanese Americans elected in midterms
Iran sanctions won't hit Lebanon: bankers
US Treasury keeps squeezing Hezbollah's cash stream
Sfeir urges stability for country's prosperity
New Cabinet should lower deficit: economist


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DUBLIN--(BUSINESS WIRE)--The "Global Sleep Apnea Market (By Products - Diagnostics & Therapeutics; By Region - North America - The US; Europe - The UK & Germany; Asia Pacific - China & India; Latin America) Outlook 2024" report has been added to ResearchAndMarkets.com's offering.
The growth of global sleep apnea devices market is primarily attributed to the prevalence of sleep apnea, high incidence of lifestyle-related chronic diseases, increasing obesity, rising demand in emerging markets and increasing geriatric population. However, some of the factors restraining the growth of the industry are stringent regulatory norms and the high cost of devices.
The report provides information on the current scenario, market outlook of the global sleep apnea market with detailed analysis of market segments such as Diagnostics & Therapeutics.
The market is further analyzed with the detailed market outlook for global as well as regional markets such as North America, Europe, Asia Pacific and Latin America. Future forecasts of sleep apnea treatment market overall and across various sub-segments have been provided till 2024, for all the geographies.
Furthermore, major industry players have been prudently analyzed in the competitive landscape section of the report in order to provide key comparative insights.
Major industry players operating in the global sleep apnea market include ResMed Inc., Fisher & Paykel Healthcare, Philips Respironics, CareFusion, among others. These players are profiled herein based on attributes such as business overview, product segments, and financial analysis.
It also compiles performance comparison of aforementioned companies and other leading companies in the segment based on various parameters in the competitive landscape section.
In totality, the report provides detailed market analysis, with relevant forecasted data supported by key market dynamics. This information will be helpful in evaluating opportunities in the global as well as regional sleep apnea market.
Key Topics Covered
1. Executive Summary
2. Research Methodology
3. Sleep Apnea
4. Market Analysis
5. Market Segmentation
6. Regional Analysis
7. Market Dynamics
8. Competitive Landscape
9. Company Profiles
- ResMed Inc.
- Fisher & Paykel Healthcare
- Philips Respironics
- CareFusion
For more information about this report visit https://www.researchandmarkets.com/research/l62gmn/global_sleep?w=4


text:
The little, square, box with the number buttons and flashing lights screams at me.
It breaks the morning's stillness with is harsh tone.
"Hello, how may I help you…"
Words now blasting out of the speaker I hold clenched.
The little, square, box tries to tell me what to do.
If I follow through with the instruction I've just received,
Many people will be unable to move forward.
Many will be stranded.
Other little, square boxes will awaken:
The chain reaction will begin.
I must choose
how to react…
Do I rely on experiences from the past?
Or, do I blaze a new cognitive path?
Create new synaptic links…
Play or pass?
Decide or stand by?
Make impact?
Or watch the house of cards
sway in the breeze…


text:
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Proctor : March 2016
40 PROCTOR | March 2016 Signing of the times What about contracts and deeds? 'Electronic signatures' can include a scanned image of a signature inserted into a document, a typed name or a digital signature created using public key infrastructure, or a combination of these. There are several cloud-based electronic signing services available. Some use typed signatures. For example, the service may allow you to upload a document to an electronic signing website, then email a person a website link to the document for them to sign. When they click the link they are taken to a website page with the document. It contains a line and an 'x' for them to sign, but on the line is a box which states 'click to sign'. The person can type their name and choose a variety of fonts with appearances similar to handwriting. They can then click 'apply' and their name appears in that font on the signature line. If the person needs to sign in other places, they can click in the other places in the document to insert the same signature. Public key infrastructure is a more secure form of signing. When you sign a document using a digital signature, you cryptographically sign the document with your private encryption key which you keep secret. In practice, you might insert a USB key containing your private key and enter a PIN to run the encryption. The recipient decrypts the signature with a corresponding public key and checks with the key certification authority that the key has not been revoked. If you lose your key, you tell the key certification authority so it can revoke the key and can tell people that the key has been revoked. Legal requirements for signatures There is no requirement under the common law for a contract to be in writing and signed. You can make most contracts through a spoken agreement. However, it's prudent to ensure that contracts are in writing to confirm what has been agreed and that they are signed to confirm that parties are bound. Legislation requires certain contracts to be in writing and signed. The most well-known is the Statute of Frauds legislation that requires writing for guarantees and dispositions of land signed by the guarantor or seller, in sections 56 and 59 of the Property Law Act 1974. What satisfies a statutory requirement for writing and a signature is a matter of statutory interpretation. 'Writing' is defined in schedule 1 of the Acts Interpretation Act 1954 to include any mode of representing or reproducing words in a visible form. An email or a document in some other electronic format, such as a PDF file, can satisfy the requirements for writing in a Queensland Act, subject to any contrary intention appearing in the Act.1 'Sign' has been held to mean "affixing in some way, whether by writing with pen or pencil or by otherwise impressing upon a document, one's name or 'signature' so as personally to authenticate the document". 2 Affixing a rubber stamp can be sufficient. A name typed in an email can also be sufficient.3 Doubt about whether an electronic signature is effective can also be removed by electronic transactions legislation. Section 14(1) of the Electronic Transactions (Queensland) Act 2001 provides: 14 Requirement for signature (1) If, under a State law, a person's signature is required, the requirement is taken to have been met for an electronic communication if— (a) a method is used to identify the person and to indicate the person's intention in relation to the information communicated; and (b) the method used was either— (i) as reliable as appropriate for the purposes for which the electronic communication was generated or communicated, having regard to all the circumstances, including any relevant agreement; or (ii) proven in fact to have fulfilled the functions described in paragraph (a), by itself or together with further evidence; and (c) the person to whom the signature is required to be given consents to the requirement being met by using the method mentioned in paragraph (a). In Stellard Pty Ltd v North Queensland Fuel Pty Ltd [2015] QSC 119, 4 an email was held to meet the requirement for writing signed by a seller in s59 of the Property Law Act. Martin J indicated that the requirement in s14(1)(b) was met because the person signing could be identified and their intention could be established by evidence made up of various conversations before the email was sent together with an admission in the pleadings about who sent the email. Signing by companies Under s127(1) of the Corporations Act 2001 (Cth), a company may execute a document by having two directors or a director and secretary of the company sign the document.5 Under s129(5) of the Corporations Act, a person can assume that a document has been duly executed if it appears to be executed in accordance with s127(1). The definition of 'document' in s2B of the Acts Interpretation Act 1901 (Cth) includes anything from which writings can be reproduced. A document can therefore include a computer system which can display the document. 'Sign' is not defined in the Corporations Act. It is seems likely that it would include an electronic signature but there do not appear to be any cases on the issue. The provisions of the Electronic Transactions Act 1999 (Cth) about electronic signatures do not apply to the Corporations Act.6 It is therefore not possible to rely on the Electronic Transactions Act to deem that the requirement for a signature under s127(1) of the Corporations Act has been met. A company can execute a contract through an agent. Section 136 of the Corporations Act provides that a company's power to make a contract may be exercised by an individual acting with the company's express or implied authority. The Corporations Act does not say how the agent must make the contract or that they can sign electronically. For significant contracts, parties often insist on signing under s127(1) so that it is possible to rely on the assumption in s127(5) and insist on the cautious approach of printing the document and signing it manually. Witnessing of contracts There is no requirement under the common law for contracts to be witnessed. It is not unusual for the parties to a contract to provide for signatures to be witnessed however, because it might help resist any potential claims by a party signing that it was fraudulently signed by someone else. There are practical issues to overcome if electronic witnessing is to be as effective for this purpose as manual witnessing. back to contents
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text: This is the perfect place to stay in SMA. Although it's close to EVERYTHING, it is hidden away in a beautiful courtyard so it is private and quiet. The hosts are friendly and kind. A very comfortable little home, everything you need for a couple or single person. King size bed is clean and comfortable. Private little garden to enjoy. Totally recommend this little jewel.