# Joachim DomstaThe State University of Applied Sciences in Elbląg, · The Institute of Applied Informatics

Joachim Domsta

Dr Hab.

## About

41

Publications

109,622

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237

Citations

Citations since 2016

Introduction

The research interests and works are focussed on:
1. building and analysing rigorous mathematical models of real phenomena, especially dynamical systems describing evolution of physical, biological, chemical, economical and any other types of real objects;
2. mathematical methods applicable to the analysis of the models under investigations - functional and differential equations, stochastic processes.

Additional affiliations

October 2003 - October 2003

## Publications

Publications (41)

A construction contradicting the so called "new stability theorem" by Itzhak Barkana

Based on the solutions of the Schroedinger equation for free (non-relativitic) motion of a single particle, the Feynman path integral is derived with the use of propertis of the Fourier transformation. Extension to motions accelerated by potential forces is sketched. The case of quadratic potential is analysed in details.

LT transformation of EM fields; deriving Biot-Savart formula from electrostatic Coulomb field of a point-charge at rest.

The fundamentals of the expanding spherically symmetric escape speed Susskind model of the (not necessarily homogeneous) universe based on Newtonian gravity are considered in detail. A rigorous formulation of the evolution for the case of finite mass of the universe is presented. Every escape speed model is uniquely characterized by the time depend...

special relativity theory-models with gravity (srt+g) 4. Another derivation of the proper acceleration (for subluminal motions) Joachim Domsta The current essay is the fourth part of the project SRT models with gravity. The preceding parts are: SRT+G 1. (file and comments) A derivation of the formula for electrostatic potential of a spherically sym...

Current essay is the third part of the project Special Relativity Theory - models with gravity (SRT+G 3)). The aim of the project is to obtain some acceptable mathematical model of gravity forces in the flat Minkowski space, thus our first important step is to find reasonable necessary conditions to be fulfilled by the fields of accelerations. We p...

Potentials for a physically appropriate description of the gravitational and the electrostatic fields may possess the following alleged "failures"
- in some points their gradient and/or Laplacian does not exsist;
- they are unbounded and/or do not possess limit at some points or at infinity;
- in some cases the formula consists of many parts to cov...

The note contains a solution of the following Problem:
Find all electrostatic potentials Φ : R^3 → R of the field E : R^3 → R^3 of forces intensity generated by a charge with spherically symmetric distribution determined by a bounded integrable density µ : R^3 → R expressed via a given function m : R_+ → R as follows µ({\bf r}) =: m(r) for |{\bf r...

We consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offspring’s trait is equal to an additively perturbed arithmetic me...

Adiabatic potential energy curves of the $^1\Sigma^+$ and $^1\Pi$ states of the LiH molecule have been calculated. They correlate asymptotically to atomic states, like 2s+1s, 2p+1s, 3s+1s, 3p+1s, 3d+1s, 4s+1s, 4p+1s and 4d+1s. Very good agreement is found between our calculated spectroscopic parameters and experimental ones. The dynamics of the rot...

Complete analysis of the regular variability of functions in a single variable in relation to linear functional equations and applications to regular iteration is presented. In particular, extension of the Szekeres-Lundberg pprincipal function (originally applied for the Schro"der equation) and Burek-Coifman-Kuczma-Seneta principal function (applie...

A matrix of complex numbers is said to be semi-stochastic if for every column the sum of elements equals one. With the use of unitary semi-stochastic matrices a multi-instant quantum pure states are introduced. For two instants, say 0 and 1, a pure state at instant 0 represented by a unit vector $\Psi^{(0)} = [ \psi^{(0)}_1, \psi^{(0)}_2, \dots, \p...

We study the weak convergence of iterates of so-called centred kernel
quadratic stochastic operators. These iterations, in a population evolution
setting, describe the additive perturbation of the arithmetic mean of the
traits of an individual's parents and correspond to certain weighted sums of
independent random variables. We show that one can ob...

Two selfmappings (Formula presented.) and (Formula presented.) of the open interval (Formula presented.) are said to be regularly conjugate with respect to the distinguished end-point (Formula presented.) whenever for some uniformly regularly varying at (Formula presented.) bijective selfmapping (Formula presented.) we have (Formula presented.). Le...

I.Two ways of obtaining (possibly, non-Markovian) evolution of a quantum system, say S, are compared:
- the most natural one leads by reduction of a unitary evolution of a supersystem, say (S; R), i.e. when S is
coupled to a reservoir R
- and the way by averaging random unitary dynamics of system S alone (the considered random dynamics is
introduce...

A consistent dfinition of measurement of a quantum system by its subsystem is proposed.
The results of the measurement are analysed in relation to properties of the interaction
Hamiltonian between the subsystems. The product form of Hamiltonians is assumed.
It is shown by examples, that non-commuting factors ensure more reach information
read by a...

The Hamiltonians of the considered bi-partite systems are of the form H SR =H S ⊗1 R +Q S ⊗M R +1 S ⊗H R · Subindex S corresponds to the observed system and R to the reservoir (the enviroment of S). Two classes of systems are distinguished: the discrete-continuous (D-C) and the continuous-continuous (C-C) models. In both cases resevoir operators M...

Some simple examples of quantum systems are collected to illustrate requirements suffi-cient for the evolution of a subsystem according to a quantum dynamical semigroup. For this, a class of quantum dynamics of a system S coupled to a reservoir R is analyzed in the Hilbert space H SR = H S ⊗ H R , where H R = L 2 (R) and H S = l 2 I , with I standi...

For a continuous and strictly monotonic function f defined on an interval I of positive reals, the function
Mf ( x,y ) = f - 1 ( \fracxf(x) + yf(y) x + y ),x,y Î I M_{f} {\left( {x,y} \right)} = f^{{ - 1}} {\left( {\frac{{xf(x) + yf(y)}} {{x + y}}} \right)},x,y\, \in {I}
is a mean. Assuming that at least one of f and g is four times continuously...

For a bijective $\phi : (0,1) \to (0,1)$, and two constants $a, b > 0$, let $g : (0,1) × (0,1) \to (0,1)$ be a pseudo-mean defined as follows, (*) $g(x, y) := \phi^{-1} (a ·\phi(x) + b · \phi(y))$ , for $x, y \in (0,1)$ . The following fact is proved: For every pair of $a$ and $b$, function $g$ determines $\phi$ uniquely, up to a multiplicative con...

Leth be a selfmapping ofR
+ h is a homeomorphism without fixed points and 1 < Dh < ¥,h is a homeomorphism without fixed points and 1< Dh< \infty ,
((Z))whereDh
ht ( x ) = ht,¥ ( x ): = limn ® ¥ hn (dt h - n (x)),x Î \mathbbR+ ,where = Dh,h_t \left( x \right) = h_{t,\infty } \left( x \right): = \mathop {\lim }\limits_{n \to \infty } h^n (d^t \cdot...

Let n X (.) , n ∈ N , be a sequence of homogeneous semi-Markov processes (HSMP) on a countable set K, all with the same initial p.d. concentrated on a subset J, ∅ = J ⊂ K J = K. The subrenewal kernels which are restrictions of the corresponding renewal kernels n Q on K × K to J × J are assumed to be suitably convergent to a renewal kernel P (on J ×...

Norms of the embeddings of AC_q into L_p(I) are given for 0 < p \le \infty. They are known from the results by V.M. Tichomirov (1975) for 1 \le p \le \infty. The extreme functions are expressed explicitly in terms of the beta distribution functions.The results apply to an extension of the functional H.Finkelstein's LIL (1971). Similar results were...

A differential equation of the radiance reflectance is derived. It is valid for horizontally homogeneous vertically stratified layers, i.e. when the inherent parameters depend on the depth only. The considerations apply to any monochromatic radiation with arbitrary angular distribution; the azimuthal invariance is not required. For homogeneous laye...

Estimating the reliability function of the renewed system based on the data before the renewal (in Polish)
https://yadda.icm.edu.pl/yadda/element/bwmeta1.element.ojs-doi-10_14708_ma_v11i22_1585/c/1585-1492.pdf

It is shown that the joint unconditional density function of demand and supply is a computable function of parameters of the conditional density function of the observed quantity. Propositions of formulating unconditional and conditional disequilibrium measures are suggested.

The paper presents a phenomenological model of the effect of capture of dispergated phase particles in fissures during a flow of suspension through those fissures. The flow of the diphase liquid and related phenomena are treated as the flow of a homogeneous liquid through a region of variable geometrical structure. The particlesof different sizes c...

Spline interpolating basis in C^k(I) is constructed for k=2m+2, with m=-1,0,... The splines are of degree k+1 (without defect). The end conditions for the interpolating splines depend only on the values of the expanded function, not on its derivalives. It follows that the constructed sequence of splines of degree k+1 is simultaneously a basis in al...

Full text available also at:
http://ictp.acad.ro/jnaat/journal/article/view/1976-vol5-no1-art1

In the theory presented the following phenomena have been analysed from a uniform point of view: 1) concentration quenching 2) quenching by foreign absorbing substances 3) concentration depolarization of photoluminescence. The participation of primarily unexcited molecules of the donor in the process of energy transfer to the molecules of the accep...

ABSTRACT: In the theory presented the following phenomena have been analysed from a uniform point of view: 1) concentration quenching 2) quenching by foreign absorbing substances 3) concentration depolarization of photoluminescence. The participation of primarily unexcited molecules of the donor in the process of energy transfer to the molecules of...

Original title: O dwóch przedstawieniach funkcji giętych

The quenching of photoluminescence by foreign ab-sorbing substances may be described by the following, well-known expression, obtained by FÖRSTER as well as by other authors independently. . .
Recently we have obtained the following expression for the relative quantum yield of the donor's photoluminescence . . . .
the full text is available also a...

## Questions

Questions (4)

## Projects

Projects (4)

The project "SRT models with gravity" is open for showing in front of interested researchers, also with their participation, to what extend one can estimate (calculate approximately) some features of relativistic motion described as geodesics in the GR by suitably chosen gravity forces in flat Minkowski space. The pattern examples of problems of this type are the perihelion motion of planets moving on almost elliptical orbits, and the motion with constant acceleration. One of the aims is to establish which assumption leads to better comparison: "gravitational mass equals the relativistic mass" or "gravitational mass equals the rest mass".

Research and pedagogical contributions to celebrated mathematical themes. Solving a few types of problems by means of elementary techniques.