We present efficiently verifiable sufficient conditions for the validity of specific NPhard semi-infinite systems of linear matrix inequalities (LMIs) arising from LMIs with uncertain data and demonstrate that these conditions are “tight” up to an absolute constant factor. In particular, we prove that given an n × n interval matrix Uρ = {A | |Aij − Aij | ≤ ρCij}, one can build a computable lowe...

The new symmetry of the loop dynamics of QCD is found. This is a local SUSY s = (s); = (s) of the superloop eld X (s; ) = x (s) + (s). The remarkable thing is, there is no einbein-gravitino on this theory, which makes it a 1D topological supergravity, or locally SUSY quantum mechanics. Using this symmetry, we derive the large Nc loop equation in momentum superloop space. Introducing as before t...

A polynomially parametrized family of continuous-time controllable linear systems is always stabilizable by polynomially parametrized feedback. 1. RESULTS Theorem 1. Let (Aλ,Bλ) be a pair of matrices, all whose entries are real polynomial functions of the parameter λ∈Rr. Assume that Aλ is n×n , Bλ is n×m, and that the pair (Aλ,Bλ) is controllable for each λ∈Rr. Then, there exists an m×n matrix ...

= −divax, t∇u + b⃗x, t ⋅ ∇u + cx, tux, t with aij, bj, c ∈ LUT and for a0 > 0, z⃗ ⋅ aijx, t z⃗ ≥ a0 | z⃗| ∀z⃗ ∀x, t ∈ UT. Then L is said to be uniformly elliptic on UT. We recall that the assumptions on the coefficients aij, bj, c, imply the existence of positive constants, a1,a0 and μ0 such that for all u,v ∈ H1U, and μ > μ0, |Bu,v, t| ≤ a1‖u‖1‖v‖1 a.e. t ∈ 0,T Bu,u, t +...

For a matrix A = [aij ] m,n i,j=1 ∈ Fm×n, the transpose of A is the matrix A> = [aji] n,m j,i=1 ∈ Fn×m. A square matrix A ∈ Rn×n is called symmetric if aji = aij for all i, j ∈ {1, . . . , n} and is called skew-symmetric or anti-symmetric if aji = −aij for all i, j ∈ {1, . . . , n}. A basis will be denoted B = {u1,u2, . . . ,un} when the ordering of the basis vectors is not important and B = [u...

The new symmetry of the loop dynamics of QCD is found. This is a local SUSY δs = θβ(s), δθ = β(s) of the superloop field Xμ(s, θ) = xμ(s) + θψμ(s). The remarkable thing is, there is no einbein-gravitino on this theory, which makes it a 1D topological supergravity, or locally SUSY quantum mechanics. Using this symmetry, we derive the large Nc loop equation in momentum superloop space. Introducin...

This is a short survey paper based on the topics of the author’s research along with his collaborators. Main topics presented in the paper are on the regularity and rigidity theorems for the solutions of the elliptic differential equations. In particular, the author poses several open problems in these topics for further study. The paper contains six sections. Regularity theorems for the ellipt...

Let Bn be an aperiodic Brandt semigroup M0[G;n, n;P ] where G is the trivial group, n ∈ N and P = (aij)n×n with aij = 1G if i = j and aij = 0 otherwise. The maximum size of an independent set in Bn is known to be bn2/4c+n, where bn2/4c denotes the largest integer not greater than n2/4. We reprove this result using Turán’s famous graph theorem. Moreover, we give a characterization of all indepen...

Using Ephestia kuehniella larvae as hosts, invert emulsion (IE) and an aqueous suspension (AS) of Beauveria bassiana (isolate IR34-JS2) and Metarhizium anisopliae (isolate IR41-TT1) formulations were compared when stored for three months at either 3 °C or 25 °C. Initially, IE formulations of isolates JS2 and TT1 were 13- and 14-fold more virulent than AS formulations, based on their LC50 values...

Let A = {A1, . . . , Ar} be a partition of a set {1, . . . , m} × {1, . . . , n} into r nonempty subsets, and A = (aij) be an m × n matrix. We say that A has a pattern A provided that aij = ai′j′ if and only if (i, j), (i, j) ∈ At for some t ∈ {1, . . . , r}. In this note we study the following function f defined on the set of all m × n matrices M with s distinct entries: f(M ;A) is the smalles...