4. Spatial Point Processes with Dependent Marks for Fingerprint Minutiae. Let xn ≡ { xi, i = 1, 2, · · · , n } denote the collection of n minutiae locations, and for each x ∈ xn, the minutiae orientation wx denotes the corresponding mark, which takes values in (0, π]. The distribution of minutiae in a fingerprint image is best described in terms of a hierarchical model involving all random enti...

A semiclassical calculation of particle production by a scalar field in a potential is performed. We focus on the particular case of production of fermions by a NambuGoldstone boson θ. We have derived a (non)local equation of motion for the θ-field with the backreaction of the produced particles taken into account. The equation is solved in some special cases, namely for purely Nambu-Goldstone ...

cos nθ cos mθ = 2 cos(n − m)θ + 2 cos(n + m)θ. Certain classical orthogonal polynomials admit explicit computation of the coefficients c(n,m, k). For example, they are known explicitly for the ultraspherical polynomials along with their q-analogs [8]. However, they are not available in a simple form for the nonsymmetric Jacobi polynomials (see [7]). The first general criterion for nonnegativity...

Quantum metrology bears a great promise in enhancing measurement precision, but is unlikely to become practical in the near future. Its concepts can nevertheless inspire classical or hybrid methods of immediate value. Here we demonstrate NOON-like photonic states of m quanta of angular momentum up to m=100, in a setup that acts as a 'photonic gear', converting, for each photon, a mechanical rot...

We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

Let $G$ be a connected graph on $n$ vertices. $G$ is called tricyclic if it has $n + 2$ edges, and tetracyclic if $G$ has exactly $n + 3$ edges. Suppose $mathcal{C}_n$ and $mathcal{D}_n$ denote the set of all tricyclic and tetracyclic $n-$vertex graphs, respectively. The aim of this paper is to calculate the minimum and maximum of eccentric connectivity index in $mathcal{C}_n$ and $mathcal{D}_n...

In this paper we study the homogeneous conic system F : Ax = 0, x ∈ C \ {0}. We choose a point s̄ ∈ intC∗ that serves as a normalizer and consider computational properties of the normalized system Fs̄ : Ax = 0, s̄T x = 1, x ∈ C. We show that the computational complexity of solving F via an interior-point method depends only on the complexity value θ of the barrier for C and on the symmetry of the ...

the divisibility graph $mathscr{d}(g)$ for a finite group $g$ is a graph with vertex set ${rm cs}(g)setminus{1}$‎ ‎where ${rm cs}(g)$ is the set of conjugacy class sizes of $g$‎. ‎two vertices $a$ and $b$ are adjacent whenever $a$ divides‎ ‎$b$ or $b$ divides $a$‎. ‎in this paper we will find the number of connected components of $mathscr{d}(g)$ where $g$ is a‎ ‎simple zassenhaus group or an sp...

at present paper, we establish the existence of pullback $mathcal{d}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $l^2(mathbb{r}^n)times l^2(mathbb{r}^n)$. in order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{d}$-absorbing set, is pullback $widehat{d}_0$-asymptotically compact.

‎‎For a finite group $G$ and a subgroup $H$ of $G$‎, ‎the relative commutativity degree of $H$ in $G$‎, ‎denoted by $d(H,G)$‎, ‎is the probability that an element of $H$ commutes with an element of $G$‎. ‎Let $mathcal{D}(G)={d(H,G):Hleq G}$ be the set of all relative commutativity degrees of subgroups of $G$‎. ‎It is shown that a finite group $G$ admits three relative commutativity degrees if a...