and Applied Analysis 3 holding for any t ∈ 0, T . Here ( a ij x e j k ) t : ∫ t 0 a ij x, t, τ · e j k x, τ dτ 2.4 are Volterra integral operators with kernels a ij x, t, τ ; a hk ij 0 x, t are instantaneous elastic coefficients out-of-integral terms and a ij x : a hk ij 0 x, t a ij x ; fi0 are components of a vector of external forces; φi x, t are components of a vector of boundary traction on...

For $m,n\in\mathbb{N}$ let $X=(X_{ij})_{i\leq m,j\leq n}$ be a random matrix, $A=(a_{ij})_{i\leq real deterministic and $X_A=(a_{ij}X_{ij})_{i\leq the corresponding structured matrix. We study expected operator norm of $X_A$ considered as between $\ell_p^n$ $\ell_q^m$ for $1\leq p,q \leq \infty$. prove optimal bounds up to logarithmic terms when underlying matrix $X$ has i.i.d. Gaussian entries...

(A) Let Q(A) be number of comparisons done on input array A: (A) R ij : event that rank i element is compared with rank j element, for 1 ≤ i < j ≤ n. (B) X ij is the indicator random variable for R ij. That is, X ij = 1 if rank i is compared with rank j element, otherwise 0. (B) Q(A) = ∑ 1≤i<j≤n X ij. (C) By linearity of expectation,

The effective chiral interaction between molecules arising from long-range quantum interactions between fluctuating charge moments is analyzed in terms of a simple model of chiral molecules. This model is based on the approximations that (a) the dominant excited states of a molecule form a band whose width is small compared to the average energy of excitation above the ground state and (b) biax...

Inspired by the recent observation of $\chi_{c0}(3930)$, $X(4685)$ and $X(4630)$ LHCb Collaboration some exotic resonances such as $X(4350)$, $X(4500)$, etc. several experiment collaborations, $cs\bar{c}\bar{s}$ tetraquark systems with $IJ^{P}=00^+$, $01^+$ $02^+$ are systematically investigated in framework quark delocalization color screening model(QDCSM). Two structures, meson-meson diquark-...

We develop a novel eikonal expansion for the Cooperon to study the effect of spaceand time-dependent electric fields on the dephasing rate of disordered conductors. For randomly fluctuating fields with arbitrary covariance we derive a general expression for the dephasing rate which is free of infrared divergencies in reduced dimensions. For time-dependent external fields with finite wavelength ...

We consider the free non-commutative analogue , introduced by D. Voiculescu, of the concept of Fisher information for random variables. We determine the minimal possible value of (a; a), if a is a non-commutative random variable subject to the constraint that the distribution of a a is prescribed. More generally, we obtain the minimal possible value of (fa ij ; a ij g 1i;jd), if fa ij g 1i;jd i...

A sign pattern is a matrix with entries in {+, −, 0}. A full sign pattern has no zero entries. The refined inertia of a matrix pattern is defined and techniques are developed for constructing potentially nilpotent full sign patterns. Such patterns are spectrally arbitrary. These techniques can also be used to construct potentially nilpotent sign patterns that are not full, as well as potentiall...