Nonlocal Operational Calculi for Dunkl Operators

The one-dimensional Dunkl operator $D_k$ with a non-negative parameter $k$, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of $D_k$, satisfying this condition is studied. An operational calculus of Mikusinski type is developed. In the frames of this operational calculi an extension of the Heaviside algorithm for solution of nonlocal Cauchy boundary value problems for Dunkl functional-differential equations $P(D_k)u=f$ with a given polynomial $P$ is proposed. The solution of these equations in mean-periodic functions reduces to such problems. Necessary and sufficient condition for existence of unique solution in mean-periodic functions is found

Centrality evolution of the charged-particle pseudorapidity density over a broad pseudorapidity range in Pb-Pb collisions at root s(NN)=2.76TeV

Peer reviewe

Комутанти на оператора на Ойлер и съответни средно-периодични функции

[Dimovski Ivan H.; Dimovski Ivan Hristov; Димовски Иван Христов]; [Hristov Valentin Z.; Hristov Valentin Zdravkov; Христов Валентин Здравков

Нелокални операционни смятания за оператори на Дънкъл

[Dimovski Ivan H.; Димовски Иван Х.]; [Hristov Valentin Z.; Христов Валентин 3.]2000 Mathematics Subject Classification: 44A40; 44A35; 34K06

Комутанти на оператора на Помие

[Dimovski Ivan H.; Dimovski Ivan Hristov; Димовски Иван Христов]; [Hristov Valentin Z.; Hristov Valentin Zdravkov; Христов Валентин Здравков

Commutants of the Pommiez operator

The Pommiez operator (Δf)(z)=(f(z)−f(0))/z is considered in the space ℋ(G) of the holomorphic functions in an arbitrary finite Runge domain G. A new proof of a representation formula of Linchuk of the commutant of Δ in ℋ(G) is given. The main result is a representation formula of the commutant of the Pommiez operator in an arbitrary invariant hyperplane of ℋ(G). It uses an explicit convolution product for an arbitrary right inverse operator of Δ or of a perturbation Δ−λI of it. A relation between these two types of commutants is found

Комутанти на операторите на Дънкъл в С(R)

[Dimovski Ivan H.; Димовски Иван Х.]; [Hristov Valentin Z.; Христов Валентин 3.]; [Sifi Mohamed; Сифи Мохамед

Direct observation of the dead-cone effect in quantum chromodynamics

The direct measurement of the QCD dead cone in charm quark fragmentation is reported, using iterative declustering of jets tagged with a fully reconstructed charmed hadron

Direct observation of the dead-cone effect in quantum chromodynamics

At particle collider experiments, elementary particle interactions with large momentum transfer produce quarks and gluons (known as partons) whose evolution is governed by the strong force, as described by the theory of quantum chromodynamics (QCD) [1]. The vacuum is not transparent to the partons and induces gluon radiation and quark pair production in a process that can be described as a parton shower [2]. Studying the pattern of the parton shower is one of the key experimental tools in understanding the properties of QCD. This pattern is expected to depend on the mass of the initiating parton, through a phenomenon known as the dead-cone effect, which predicts a suppression of the gluon spectrum emitted by a heavy quark of mass m and energy E, within a cone of angular size m/E around the emitter [3]. A direct observation of the dead-cone effect in QCD has not been possible until now, due to the challenge of reconstructing the cascading quarks and gluons from the experimentally accessible bound hadronic states. Here we show the first direct observation of the QCD dead-cone by using new iterative declustering techniques [4, 5] to reconstruct the parton shower of charm quarks. This result confirms a fundamental feature of QCD, which is derived more generally from its origin as a gauge quantum field theory. Furthermore, the measurement of a dead-cone angle constitutes the first direct experimental observation of the non-zero mass of the charm quark, which is a fundamental constant in the standard model of particle physics.The direct measurement of the QCD dead cone in charm quark fragmentation is reported, using iterative declustering of jets tagged with a fully reconstructed charmed hadron.In particle collider experiments, elementary particle interactions with large momentum transfer produce quarks and gluons (known as partons) whose evolution is governed by the strong force, as described by the theory of quantum chromodynamics (QCD). These partons subsequently emit further partons in a process that can be described as a parton shower which culminates in the formation of detectable hadrons. Studying the pattern of the parton shower is one of the key experimental tools for testing QCD. This pattern is expected to depend on the mass of the initiating parton, through a phenomenon known as the dead-cone effect, which predicts a suppression of the gluon spectrum emitted by a heavy quark of mass $m_{\rm{Q}}$ and energy $E$, within a cone of angular size $m_{\rm{Q}}$/$E$ around the emitter. Previously, a direct observation of the dead-cone effect in QCD had not been possible, owing to the challenge of reconstructing the cascading quarks and gluons from the experimentally accessible hadrons. We report the direct observation of the QCD dead cone by using new iterative declustering techniques to reconstruct the parton shower of charm quarks. This result confirms a fundamental feature of QCD. Furthermore, the measurement of a dead-cone angle constitutes a direct experimental observation of the non-zero mass of the charm quark, which is a fundamental constant in the standard model of particle physics