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Within the background-field framework we present a path integral derivation of the splitting Ward identity for the one-particle irreducible effective action in the presence of an infrared regulator, and make connection with earlier works on…
In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…
The coefficient of x^{-1} of a formal Laurent series f(x) is called the formal residue of f(x). Many combinatorial numbers can be represented by the formal residues of hypergeometric terms. With these representations and the extended…
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the…
In this paper we improve drastically the estimate for the multiplicity of a binary recurrence. The main contribution comes from an effective version of the Faltings' Product Theorem.
Interpretation of unitarity saturation as reflective scattering is discussed. Analogies with optics and Berry phase alongside with the experimental consequences of the proposed interpretation at the LHC energies are considered.
In this article we prove an algebraic identity which significantly generalizes the formula for sum of powers of consecutive integers involving Stirling numbers of the second kind. Also we have obtained a generalization of Newton-Girard…
In this paper we solve combinatorial and algebraic problems associated with a multivariate identity first considered by S. Sherman wich he called an analog to the Witt identity. We extend previous results obtained for the univariante case.
Probabilistic abstract interpretation is a theory used to extract particular properties of a computer program when it is infeasible to test every single inputs. In this paper we apply the theory on neural networks for the same purpose: to…
We describe a class of spinor-curvature identities which exist for Riemannian or Riemann-Cartan geometries. Each identity relates an expression quadratic in the covariant derivative of a spinor field with an expression linear in the…
Based on an interesting identity of Bat{\i}r we derive new identities for double sums involving famous number sequences. We also prove some double sum identities for binomial transform pairs.
Finding hidden order within disorder is a common interest in material science, wave physics, and mathematics. The Riemann hypothesis, stating the locations of nontrivial zeros of the Riemann zeta function, tentatively characterizes…
A cubic identity for the Infeld-van der Waerden field is found and its application to verifying an explicit formula for the spinor components of the metric connection is demonstrated.
We discuss a few integral operators and provide expressions for them in terms of smooth functions of some natural self-adjoint operators. These operators appear in the context of scattering theory, but are independent of any perturbation…
The density of states for a finite or an infinite cluster of scatterers in the case of both electrons and photons can be represented in a general form as the sum over all Krein-Friedel contributions of individual scatterers and a…
It is shown that the quantised enveloping algebra of sl(n) contains a quantum Lie algebra, defined by means of axioms similar to Woronowicz's., This gives rise to Lie algebra-like generators and relations for the locally finite part of the…
We consider simply connected bodies or regions of finite extent in space or space-time and write conservation laws associated with the equations in Parts I-IV. We review earlier work where, for elliptic equations,the boundary value problem…
Using the example of a complicated problem such as the Cauchy problem for the Navier--Stokes equation, we show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of solutions for this…
We introduce the notion of "virtual Bergman kernel" and apply it to the computation of the Bergman kernel of "domains inflated by Hermitian balls", in particular when the base domain is a bounded symmetric domain.
We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.