Yu. Tarannikov, private communication.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....this additional length scale the prediction of crack branching strongly depends on whether or not the cohesive constitutive relation is initially linear or is initially rigid crack branching is only obtained in the case of an initially linear response. Preliminary results of Pandolfi and Yu [12] show a similar absence of crack branching in 4e 06 5e 06 6e 06 7e 06 8e 06 9e 06 time (s) 0 0.5 1 1.5 2 2.5 position (mm) 0 200 400 600 800 1000 velocity (m s) Figure 3. Crack tip position and velocity vs. time for two cohesive laws. The upper set of lines in each graph corresponds to ....

Pandolfi A., Yu C., private communications (2000).

....or givens to be used in the queries, as we mentioned above. The simplest example is the relation of linear order. Throwing in such givens obviously increases the expressive power of FO, but what is often not obvious is whether any new generic queries become expressible. Yu. Gurevich [Gur90] showed that there are = generic queries that are FO expressible over finite states with , but not without. Here is a version of his example. Let K be the class of all finite Boolean algebras with an even number of atoms. This class cannot be axiomatized within the class of finite structures by ....

Yu. Gurevich, Private communication, 1990.

....(LSM) 13] chiral perturbation theory (ChPT) 14,15] and the Skyrme model [16] focused on the scalar polarizabilities and the spin independent VCS amplitude. 2 In the meantime, the vector polarizabilities have been evaluated on the basis of ChPT [17,18] and in a coupled channel unitary model [19]. The present contribution completes our earlier work on the LSM [13] by presenting the results for the vector polarizabilities. Since the model is chirally invariant, we expect similar results as in ChPT for Q 2 0, and in addition a reasonable estimate for the Q 2 dependence of the ....

A. Yu. Korchin and O. Scholten, private communication.

....any monomial w 2 M has at most one L Gammainvolutive divisor in U . Proof This follows immediately from the property (iv) of involutive division. In terms of Definition 3.2 it means that uL(u; U) vL(v; U) for all distinct u; v 2 U , if U is involutively autoreduced. 6 Proposition 3. 10 [17]. If a set U is autoreduced with respect to Pommaret division, then for any u 2 U M P (u; U) M J (u; U) and NM J (u; U) NM P (u; U) respectively. Proof Let u = x d 1 1 Delta Delta Delta x d k k 2 M be a monomial with d k 0 and v 2 U be its Pommaret divisor. Then, as follows from the ....

....i OE v) NF L (f Delta x i ; F ) 0 ] 15) 7 Grobner Bases and Involutive Bases In [13, 14] it was shown that a Pommaret basis, that is, involutive basis for Pommaret division, is also a Grobner basis, though, generally, not the reduced one. A similar property of a Janet basis was noticed in [17]. The following theorem shows that such a relation holds for any involutive division. Theorem 7.1 If set F is L Gammainvolutive, then the equality of the conventional and L Gammanormal forms (8p 2 R) NF (p; F ) NF L (p; F ) 16) holds for any normal form algorithm. Proof To prove the ....

Zharkov A.Yu. (1994b). Private communication.

....Perturbations are added to the inverse of diagonal elements to avoid small pivots, and thus control the size of the elements in the L and U factors. We use a two level block ILU strategy called BILU(0) SVD(ff) that uses a modified singular value decomposition to invert the blocks [150]. When a block A = U SigmaV T needs to be inverted, it is replaced by the perturbed inverse M = V Sigma Gamma1 U T , where Sigma is Sigma with its singular values thresholded by ffoe 1 , a factor of the largest singular value. Table 3.4 shows the results, using a block size of 4. ....

....For block incomplete factorizations, the pivot is a block. The equivalent of a small pivot in this case is a block that is very poorly conditioned, with an inverse that has very large entries. It is possible to perform a shift for a block by shifting its singular values away from zero [150]. Given the singular value decomposition of a block A = U SigmaV T , a shifted inverse A Gamma1 V Sigma Gamma1 U T (5.5) can be produced, where Sigma is Sigma with its singular values thresholded by a function of the largest singular value, such as ffoe 1 , where 0 ff 1 is a ....

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A. Yu. Yeremin. Private communication, 1995. 163

....and was followed by numerous extensions and applications[44, 111, 112, 87, 47, 48] all achieving polynomial advantage over classical algorithms. A promising new branch in quantum complexity theory is the study of a class of problems which is the quantum analog of the complexity class NP[126]. Another interesting direction in quantum computation is concerned with quantum computers simulating efficiently other physical systems such as many body Fermi systems[203, 1, 197, 42] This direction pursues the original suggestion by Feynman[93] who noticed that quantum systems are hard to ....

A. Yu. Kitaev, private communication

.... is, an ellipsoid without axis of equal length) is much more complicated than the study of the non circular elliptic billiard before, because the explicit expression of the biasymptotic motions in the first case requires the use of analytical tools much more sophisticated than in the second one [Fed97]. Therefore, in order to gain insight into the problem, it is interesting to consider a setting to which the arguments of the planar case can be easily adapted. This setting is provided by prolate ellipsoids (that is, ellipsoids with all its axis of equal length except one, which is larger) In ....

Yu. Fedorov, 1997. Private communication.

....properties of the discretization technique described above can be found in e.g. 4, 9] for the case where the underlying measure is absolutely continuous with respect to Lebesgue measure. The proof of convergence to so called SBR measures in a more general setting is currently under investigation ([10]) b) We remark that there is also a deterministic exhaustion technique to approximate P h . This method has been developed in [5] 7 Computation algorithm The strategy for the approximation of an invariant measure supported on a relative global attractor can now be formulated as follows: ....

Yu. Kifer. Private communication (1996).

....givens are considered to be a part of the domain rather than of the database scheme and to have a fixed meaning. Throwing in such givens does obviously increase the expressive power of FO, but what is often not obvious is whether any new generic queries become expressible. Yu. Gurevich [Gur90] showed that there are = generic queries that are FO expressible with over finite states, but not without . Here is a version of his example. Let K be the class of all finite Boolean algebras with an even number of atoms. This class cannot be axiomatized within the class of finite ....

Yu. Gurevich, Private communication, 1990.

....[24, 37] For block incomplete factorizations, the pivot is a block. The equivalent of a small pivot in this case is a block that is very poorly conditioned, with an inverse that has very large entries. It is possible to perform a shift for a block by shifting its singular values away from zero [43]. Given the singular value decomposition of a block A = U SigmaV T , a shifted inverse A Gamma1 V Sigma Gamma1 U T (9) can be produced, where Sigma is Sigma with its singular values thresholded by a function of the largest singular value, such as ffoe 1 , where 0 ff 1 is a ....

A. Yu. Yeremin. Private communication, 1995.

....th) 1 (1 Gamma toe x (h) 2 D 2 F (x) Theorem 7.1 shows that the Hessian norms are compatible all the way up to boundary, not just inside the Dikin ellipsoid. It follows directly from Theorem 6.1. It is interesting that these two results are actually equivalent, as shown by Nesterov [21]. Theorem 7.2 (Nesterov) Let F be a convex, logarithmically homogeneous, and at least three times differentiable barrier function for a regular convex cone K R n . Then the function g(x) GammaDF (x) y] is convex for each h 2 K if and only if Theorem 7.1 holds true. Proof. We need only to ....

Nesterov, Yu. E. (1996). Private communication.

....U T , where Sigma is Sigma with its singular values thresholded by ff 1 oe 1 ff 2 , a constant ff 2 plus a factor ff 1 of the largest singular value oe 1 . This may produce a more stable incomplete factorization if there are many blocks to be inverted that are close to being singular [Yeremin 1995]. LP SOR, LP SSOR and LP GMRES are iterative methods used as local preconditioners. 2.3 Interface with iterative methods An object oriented preconditioned iterative method requires that matrix and preconditioner objects define a small number of operations. In BPKIT, these operations are defined ....

Yeremin, A. Yu. 1995. Private communication.

....2) 2 (l Gamma 1) l Gamma 2) 2 1 These counter examples are obtained using Viro s method of construction of real algebraic varieties with prescribed topology. The curves constructed are T curves. This class of curves was suggested to consider by O. Ya. Viro and was used by S. Yu. Orevkov [1] to show the exactness of Petrovsky inequalities p Gamma n 3k 2 Gamma 3k 2 2 n Gamma p 3k 2 Gamma 3k 2 I am very greatful to V. M. Kharlamov for the useful discussions. 2 Construction A partition of convex polygon T in convex polygons t 1 ; t s is called by convex if there ....

S. Yu. Orevkov, Private communication.

....quantized into discrete levels rather than having a distribution based on a single band approximation. An empirical and hybrid model for the QM correction in MOS structures is proposed and implemented in a two dimensional (2 D) device simulator, which combines both the van Dort and Hansch models [2]. In the vicinity of the Si SiO interface, the density of conduction band states can be expressed as (1) where the axis is perpendicular to the Si SiO interface and is introduced for the finite carrier concentration at the surface ( is the normal density of conduction band states, which is ....

Z. Yu, Stanford Univ., Stanford, CA, private communication.

....effects is presented to characterize these phenomena for the gate oxide thicknesses ranging 1.3 1.8 nm. II. CAPACITANCE SIMULATION An empirical, hybrid model for the QM correction in MOS structures has been implemented in a 2D device simulator, which combines both the van Dort and Hansch models [2]. The advantages of this model are as follows: i) elimination of the discontinuity at flatband that occurs in the van Dort model, ii) single set of parameters for different technologies. The hybrid model applies the improved van Dort model for the entire bias range (from accumulation to inversion ....

Z. Yu, private communication, 1998.

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Yu. Tarannikov, private communication.

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Yu. Tarannikov, private communication.

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A. Yu. Kitaev, private communication

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A.Yu. Grosberg, D.V. Kuznetsov, Macromolecules 26, 4249 (1993); K. Binder, private communication. 13

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Yu, L. --H., private communication.

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Yu. Norikov, private communication (1996).

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Yu. Norikov, private communication (1996).

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