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Measures Not Charging Polar Sets and Schrodinger Equations in L^p

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Acta Mathematica Sinica,English Series 2010年第2期26卷 249-264页

作者： Lucian BEZNEA Nicu BOBOC institute of mathematics "simion stoilow" of the Romanian Academy University of Pitesti Faculty of mathematics and Computer Science University of Bucharest

We study the SchrSdinger equation （q -￡）u ＋μu = f, where ￡ is the generator of a Borel right process and μ is a signed measure on the state space. We prove the existence and uniqueness results in Lp, 1 ≤p 〈∞ . Since we consider measures μcharging no polar set, we have to use new tools： the Revuz formula with fine versions and the appropriate Revuz correspondence, the perturbation （subordination） operators （in the sense of G Mokobodzki） induced by the regular strongly supermedian kernels. We extend the results on the SchrSdinger equation to the case of a strongly continuous sub-Markovian resolvent of contractions on Lp. If the measure μ is positive then the perturbed process solves the martingale problem for ￡- μ and its transition semigroup is given by the Feynman-Kac formula associated with the left continuous additive functional having μ as Revuz measure.

关键词： SchrSdinger equation LP-resolvent measure perturbation Revuz correspondence right

Relativistic Dynamics, Electromagnetic Field,and Spin, as All Quantum Effects

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Journal of Electronic Science and Technology 2017年第4期15卷 333-341页

作者： Eliade Stefanescu Center of Advanced Studies in Physics Bucharest 050711 Romania institute of mathematics “simion stoilow” of the Romanian Academy Bucharest 010702 Romania

We consider a quantum particle as a wave packet in the coordinate space. When the conjugate wave packet in the momentum space is considered, we find that the group velocities of these two wave packets, which describe the particle dynamics, are in agreement with the Hamilton equations only if in the time dependent phases one considers the Lagrangian instead of the Hamiltonian which leads to the conventional Schr?dinger equation. We define a relativistic quantum principle asserting that a quantum particle has a finite frequency spectrum, with a cutoff propagation velocity c as a universal constant not depending on the coordinate system, and that any time dependent phase variation is the same in any system of coordinates. From the time dependent phase invariance,the relativistic kinematics is obtained. We consider two types of possible interactions: 1) An interaction with an external field, by a modification of the time dependent phase differential with the terms proportional to the differentials of the space-time coordinates multiplied with the components of this field four-potential, and 2)an interaction by a deformation of the space-time coordinates, due to a gravitational field. From the invariance of the time dependent phase with field components, we obtain a mechanical force of the form of Lorentz’s force, and three Maxwell equations: The Gauss-Maxwell equations for the electric and magnetic fluxes, and the Faraday-Maxwell equation for the electromagnetic induction. When the fourth equation,Ampère-Maxwell, is considered, the interaction field takes the form of the electromagnetic field. For a low propagation velocity of the particle waves, we get a packet of waves with the time dependent phases proportional to the relativistic Hamiltonian, as in Dirac’s famous theory of spin, and a slowly-varying amplitude with a phase proportional to the momentum and this velocity. In the framework of our theory, the spin is obtained as an all quantum effect, without any additio

关键词： Group velocity Maxwell equations metric tensor quantum particle spin wave packet

New results on Cll and C12 lattices with applications to Grothendieck categories and torsion theories

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Frontiers of mathematics in China 2016年第4期11卷 815-828页

作者： Toma ALBU Mihai IOSIF simion stoilow institute of mathematics of the Romanian Academy Research Unit 5 P.O. Box 1-764 RO-010145 Bucharest 1 Romania Bucharest University Department of Mathematics Academiei Str. 14RO-010014 Bucharest 1 Romania

In this paper, which is a continuation of our previous paper [T. Albu, M. Iosif, A. Tercan, The conditions （Ci） in modular lattices, and applications, J. Algebra Appl. 15 （2016）, http： ***/10.1142/S0219498816500018], we investigate the latticial counterparts of some results about modules satisfying the conditions （Cll） or （C12）. Applications are given to Grothendieck categories and module categories equipped with hereditary torsion theories.

关键词： Modular complement lattice C12 theory element lattice upper closed element lattice Goldie dimension continuous lattice essential element uniform lattice condition (Ci) Cll socle Grothendieck category torsion

Subordination in the Sense of Bochner of Lp-semigroups and Associated Markov Processes

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Acta Mathematica Sinica,English Series 2014年第2期30卷 187-196页

作者： Oana LUPASCU simion stoilow institute of mathematics of the Romanian Academy Research group of the POSDRU Project 82514 University Politehnica of Bucharest Université Paris 13 Campus de Villetaneuse 99 av. Jean-Baptiste Clément

We show that the subordination induced by a convolution semigroup(subordination in the sense of Bochner)of a C0-semigroup of sub-Markovian operators on an Lpspace is actually associated to the subordination of a right(Markov)*** a consequence,we solve the martingale problem associate with the Lp-infinitesimal generator of the subordinate *** also prove quasi continuity properties for the elements of the domain of the Lp-generator of the subordinate *** turns out that an enlargement of the base space is necessary.A main step in the proof is the preservation under such a subordination of the property of a Markov process to be a Borel right *** use several analytic and probabilistic potential theoretical tools.

关键词： Subordination in the sense of Bochner Lp-semigroup subordinator right(Markov) process nonbranch point

Generalized Rectangular Convexity

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数学学报:英文版 2023年第9期39卷 1795-1804页

作者： Li Ping Yuan Tudor Zamfirescu School of Mathematical Sciences Hebei Normal UniversityShijiazhuang050024P.R.China Hebei International Joint Research Center for mathematics and Interdisciplinary Science Shijiazhuang050024P.R.China Hebei Key Laboratory of Computational mathematics and Applications Shijiazhuang050024P.R.China Fachbereich Mathematik TU Dortmund44221DortmundGermany institute of mathematics“simion stoilow” Romanian AcademyBucharestRomania

In this paper we investigate the tr-convexity and the rectangular biconvexity in Euclidean spaces.

关键词： tr-convex thin rectangular convexity rectangular biconvexity

Two-parameter families of uniquely extendable Diophantine triples

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Science China mathematics 2018年第3期61卷 421-438页

作者： Mihai Cipu Yasutsugu Fujita Maurice Mignotte simion stoilow institute of mathematics of the Romanian Academy Research unit nr. 5 P.O. Box 1-764 RO-014700 Bucharest Romania Department of mathematics College of Industrial Technology Nihon University 2-11-1 Shin-ei Narashino Chiba 276-0028 Japan Département de Mathematique Universite de Strasbourg Strasbourg 67084 France

Let A and K be positive integers and ε∈ {-2,-1,1,2}. The main contribution of the paper is a proof that each of the D(ε~2)-triples {K, A^2 K+2εA,(A +1)~2 K + 2ε(A+1)} has uniqui extension to a D(ε~2)-quadruple. This is used to slightly strengthen the conditions required for the existencc of a D(1)-quintuple whose smallest three elements form a regular triple.

关键词： Diophantine m-tuples Pell equations hypergeometric method linear forms in logarithms

Qualitative Analysis of Gradient-Type Systems with Oscillatory Nonlinearities on the Sierpiński Gasket

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Chinese Annals of mathematics,Series B 2013年第3期34卷 381-398页

作者： Gabriele BONANNO Giovanni MOLICA BISCI Vicentiu RDULESCU Department of Science for Engineering and Architecture (mathematics Section) Engineering Faculty University of Messina98166 Messina Italy Department Patrimonio Architettonico e Urbanistico PAU Università degli Studi "Mediterranea" di Reggio Calabria Via Melissari I-89124 Reggio Calabria Italy institute of mathematics "simion stoilow" of the Romanian Academy P. O. Box 1-764 014700 Bucharest Romania Department of mathematics University of CraiovaStreet A. I. Cuza No. 13 200585 Craiova Romania

Under an appropriate oscillating behavior either at zero or at infinity of the nonlinear data, the existence of a sequence of weak solutions for parametric quasilinear systems of the gradient-type on the Sierpinski gasket is proved. Moreover, by adopting the same hypotheses on the potential and in presence of suitable small perturbations, the same conclusion is achieved. The approach is based on variational methods and on certain analytic and geometrical properties of the Sierpinski fractal as, for instance, a compact embedding result due to Fukushima and Shima.

关键词： Sierpifiski gasket Nonlinear elliptic equation Dirichlet form WeakLaplacian

Remark on the Off-Diagonal Expansion of the Bergman Kernel on Compact Kähler Manifolds

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Communications in mathematics and Statistics 2013年第1期1卷 37-41页

作者： Xiaonan Ma George Marinescu UFR de Mathématiques UniversitéParis Diderot-Paris 7Case 701275205 Paris Cedex 13France Mathematisches Institut Universität zu KölnWeyertal 86-9050931 KölnGermany institute of mathematics‘simion stoilow’ Romanian AcademyBucharestRomania

In this short note,we compare our previous work on the off-diagonal expansion of the Bergman kernel and the preprint of Lu-Shiffman(arXiv:1301.2166).In particular,we note that the vanishing of the coefficient of p−1/2 is implicitly contained in Dai-Liu-Ma’s work(***.72(1),1-41,2006)and was explicitly stated in our book(Holomorphic Morse inequalities and Bergman *** in Math.,vol.254,2007).

关键词： Kähler manifold Bergman kernel of a positive line bundle

Subordination in the Sense of Bochner of LP-semigroups and Associated Markov Processes

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数学学报（中文版） 2014年第2期57卷 I0005-I0008页

作者： Oana LUPASCU simion stoilow institute of mathematics of the Romanian Academy Research group of the POSDRU Project 82514 PO Box 1-764 RO 014700 Bucharest Romania University Politehnica of Bucharest Splaiul Independentei nr. 313 060042 Bucharest Romania Universite Paris 13 Campus de Villetaneuse 99 av. Jean-Baptiste Clement 93430 Villetaneuse France

我们证明隶属在一个 L p 空格由 sub-Markovian 操作符的 C 0-semigroup 的卷绕旋转 semigroup (在 Bochner 的意义的隶属) 导致了实际上被联系到权利(Markov ) 的隶属进程。作为后果，我们与 L p 解决鞅问题伙伴辅助 semigroup 的无穷... 详细信息

我们证明隶属在一个 L p 空格由 sub-Markovian 操作符的 C 0-semigroup 的卷绕旋转 semigroup (在 Bochner 的意义的隶属) 导致了实际上被联系到权利(Markov ) 的隶属进程。作为后果，我们与 L p 解决鞅问题伙伴辅助 semigroup 的无穷小的生成器。我们也为辅助 semigroup 的 L p 发电机的领域的元素证明伪连续性性质。结果基础空间的增大是必要的。在证明的主要的步是在是一个 Borel 正确过程的一个 Markov 过程的性质的如此的隶属下面的保藏。我们使用几个分析、概率的潜在的理论工具。

关键词：数学数学理论数学分析数学研究论文摘要英文版