Related papers: A New Lower Bound for the Distinct Distance Consta…
We continue and generalise our earlier investigations of the number of squares in binary recurrence sequences. Here we consider sequences, $\left( y_{k} \right)_{k=-\infty}^{\infty}$, arising from the solutions of generalised negative Pell…
We consider the number of distinct distances between two finite sets of points in ${\bf R}^k$, for any constant dimension $k\ge 2$, where one set $P_1$ consists of $n$ points on a line $l$, and the other set $P_2$ consists of $m$ arbitrary…
A counter-example to lower bounds for the singular values of the sum of two matrices in [1] and [2] is given. Correct forms of the bounds are pointed out.
Given a group $G$, we say that a set $A \subseteq G$ has more sums than differences (MSTD) if $|A+A| > |A-A|$, has more differences than sums (MDTS) if $|A+A| < |A-A|$, or is sum-difference balanced if $|A+A| = |A-A|$. A problem of recent…
There is a growing literature on sums of reciprocals of polynomial functions of recurrence relations with constant coefficients and fixed depth, such as Fibonacci and Tribonacci numbers, products of such numbers, and balancing numbers…
I discuss aspects of the QCD sum rule method which attracted theorists' attention in earnest at a relatively late stage and are not yet fully solved. At first I briefly review such general topics as the structure of the operator product…
We give some results and conjectures about recurrence relations for certain sequences of binomial sums.
In this paper, we study the reciprocal sums of the Jacobsthal numbers. We establish many results on the infinite sum and alternating infinite sum of the reciprocals of Jacobsthal numbers and square Jacobsthal numbers.
In the context of boundary conformal field theory, we derive a sum rule that relates two and three point functions of the displacement operator. For four dimensional conformal field theory with a three dimensional boundary, this sum rule in…
In contrast to the existing approaches to bisimulation for fuzzy systems, we introduce a behavioral distance to measure the behavioral similarity of states in a nondeterministic fuzzy-transition system. This behavioral distance is defined…
We develop a systematic method to calculate the trace distance between two reduced density matrices in 1+1 dimensional quantum field theories. The approach exploits the path integral representation of the reduced density matrices and an ad…
This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by…
Two--sided bounds are constructed for a probability density function of a weighted sum of chi-square variables. Both cases of central and non-central chi-square variables are considered. The upper and lower bounds have the same dependence…
We evaluate the nested sum $\sum_{a_{n - 1} = c}^{a_n } {\sum_{a_{n - 2} = c}^{a_{n - 1} } { \cdots \sum_{a_0 = c}^{a_1 } {x^{a_0 } } } }$ where $a_n$ and $c$ are any integers and $x$ is a real or complex variable. Consequently, we evaluate…
We derive a QCD sum rule for the inverse moment of the $B_s$-meson light-cone distribution amplitude in HQET. Within this method, the $SU(3)_{fl}$ symmetry violation is traced to the strange quark mass and to the difference between strange…
The fractional Feynman-Kac equations describe the distribution of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, where the fractional…
We consider the small deviation probabilities (SDP) for sums of stationary Gaussian sequences. For the cases of constant boundaries and boundaries tending to zero, we obtain quite general results. For the case of the boundaries tending to…
We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…
In this paper, we provide estimates for the additive discretized energy of \[\sum_{c\in C} |\{(a_1, a_2, b_1, b_2)\in A^2\times B^2: |(a_1 +cb_1) - (a_2 + cb_2)|\le \delta\}|_{\delta},\] that depend on non-concentration conditions of the…
I derive a relation, both `forward' and `inverse', between the density and the divergence of the peculiar velocity which results from the Zel'dovich approximation. My calculations assume Gaussian initial conditions. The forward relation…