Let Sm be the set of all m×m density matrices (Hermitian positively semi-definite matrices of unit trace). Consider a problem of estimation of an unknown density matrix ρ ∈ Sm based on outcomes of n measurements of observables X1, . . . ,Xn ∈ Hm (Hm being the space of m × m Hermitian matrices) for a quantum system identically prepared n times in state ρ. Outcomes Y1, . . . , Yn of such measurem...

For any field k and any integers m,n with 0 6 2m 6 n + 1, let Wn be the k-vector space of sequences (x0, . . . , xn), and let Hm ⊆ Wn be the subset of sequences satisfying a degree-m linear recursion, i.e. for which there exist a0, . . . , am ∈ k such that

0 [GW96]. 1 [GW96]. $1.50 [Bar78d]. $11 [Bar84a]. $12.00 [Rob72]. $13 [Bar84a]. $13.00 [Rob72]. $18.50 [Jon74]. $185 [Bar79b]. $19.30 [Lan74a]. $19.50 [Dav78]. $25.00 [Pet77, And78]. 3 [BE02, FMA02]. $31-25 [Pet77]. $31.35 [Bri82]. 32 [VED06]. $35.00 [Inc86]. $39.50 [Sim83]. $58.50 [Wal81a]. $6.95 [Tho74]. 64 [AM10, VED06]. 68 [Ear76, Hol77]. $68.25 [Pit82]. $7.00 [Bar72a]. $7.50 [Bar78d]. $7.9...

Given a connected, compact, totally geodesic submanifold Ym of noncompact type inside a compact locally symmetric space of noncompact type Xn , we provide a sufficient condition that ensures that [Ym] 6= 0 ∈ Hm(X; R); in low dimensions, our condition is also necessary. We provide conditions under which there exist a tangential map of pairs from a finite cover (X̄, Ȳ) to the nonnegatively curved ...

and Applied Analysis 3 2. Problem Statements Consider the following discrete-time neural networks with interval time-varying delays: y k 1 Ay k W0g ( y k ) W1g ( y k − h k ) b, 2.1 where n denotes the number of neurons in a neural network, y k y1 k , . . . , yn k T ∈ R is the neuron state vector, g k g1 k , . . . , gn k T ∈ R denotes the neuron activation function vector, b b1, . . . , bn T ∈ R...

For real polynomials in two indeterminates a classical polynomial harmonic decomposition (cf. (1) below) is extended from square-norm divisors to conic ones. The main result is then applied to obtain a full polynomial harmonic decomposition, and to solve a Dirichlet problem with polynomial boundary data. Harmonic functions are of utmost importance in analysis, geometry, and mathematical physics...

Each solution {xn} of the equation in the title is either eventually periodic with period 3 or else, it converges to zero—which case occurs depends on whether the ratio of the initial values of {xn} is rational or irrational. Further, the sequence of ratios {xn/xn−1} satisfies a first-order difference equation that has periodic orbits of all integer periods except 3. p-cycles for each p = 3 are...

Stanniocalcin (STC), a glycoprotein hormone, is expressed in a wide variety of tissues to regulate Ca2+ and PO4- homeostasis. STC2, a member of STC family, has been reported to be associated with tumor development. In this study, we investigated whether the expression of STC2 is associated with migration and invasion of breast cancer cells. We found that breast cancer cell line 231 HM transfect...