On a Generalization of a Theorem due to Larcombe on the Sum of a 3F2 Series

MSC 2010: 33C20

On Sandwich Theorem of Analytic Functions Involving Integral Operator

2000 Mathematics Subject Classification: 30C45

The Filippov-Wazewski relaxation theorem revisited

The converse statement of the Filippov-Wazewski relaxation theorem is proven, more precisely, two differential inclusions have the same closure of their solution sets if and only if the right-hand sides have the same convex hull. The idea of the proof is examining the contingent derivatives to the attainable sets.

An Elementary Core Equivalence Theorem in a Countable Economy

We consider an infinite exchange economy with countably many traders, which can be regarded as a natural extension of finite exchange economies to an infinite one. In our countable economy the core defined in the traditional manner would be empty. To avoid this unwanted situation we have to strengthen the notion of “improves upon”. We will achieve this based on the idea that forming coalitions involve costs.

A Dalang, Morton, Willinger tétel (On the theorem of Dalang-Morton-Willinger)

In the article we shortly discuss the proof of the theorem of Dalang-Morton-Willinger. We show that the proof of the theorem depends on some interesting general properties of the stochastic convergence.

A pénzügyi eszközök árazásának alaptétele, lokálisan korlátos szemimartingál árfolyamok esetén (The fundamental theorem of asset pricing for locally bounded semimartingales)

A pénzügyi eszközök árazásának alaptétele - kissé pongyolán megfogalmazva - azt állítja, hogy egy értékpapírpiacon akkor nincs arbitrázs, ha létezik egy az eredetivel ekvivalens valószínűségi mérték, amelyre vonatkozóan az értékpapírok árait leíró folyamat egy bizonyos értelemben "martingál". Az első ilyen jellegű állítást M. Harrison és S. R. Pliska bizonyították arra esetre, amikor a valószínűségi mező végesen generált. Azóta a tételnek számos általánosítása született. Ezek közül az egyik legismertebb a Dalang{Morton{ Willinger-tétel, ami már teljesen általános valószínűségi mezőből indul ki, de felteszi, hogy az időparaméter diszkrét, és az időhorizont véges. Időközben a tételnek számos folytonos időparaméterű folyamatokra vonatkozó változata is született. Az alaptételt általános esetben, vagyis amikor valószínűségi mező teljesen általános, és az értékpapírok piaci árait leíró folyamat lokálisan korlátos szemimartingál, Delbaen és W. Schachermayer bizonyították be. A Delbaen{Schachermayer-féle alaptétel a maga nemében egy igen általános áll ítás. A tétel bizonyítása igen hosszadalmas, és a funkcionálanalízis valamint a sztochasztikus folyamatok általános elméletének mély eredményeit használja. Utóbbi tudományterület nagy részét P. A. Meyer és a francia strassbourgi iskola matematikusai dolgozták ki a 60-as évek végétől kezdve. A terület megértését tehát alaposan megnehezíti, hogy a felhasznált matematikai apparátus viszonylag friss, egy része pedig csak francia nyelven érhető el. Meggyőződésünk szerint az eredeti, 1994-es Delbaen és Schachermayer-féle bizonyítás csak kevesek által hozzáférhető. A tételnek tudomásunk szerint azóta sem született tankönyvi feldolgozása, annak ellenére, hogy maga az állítás közgazdász körökben is széles körben ismerté vált, és az eredeti cikket számos szerző idézi. Az itt bemutatott bizonyítás Delbaen és Schachermayer 1992 és 2006 közötti írásain alapul. ______ The Delbaen and Schachermayer's theorem is one of the deepest results of mathematical finance. In this article we tried to rethink and slightly simplify the original proof of the theorem to make understandable for nonspecialists who are familiar with general theory of stochastic processes. We give a detailed proof of the theorem and we give new proofs for some of the used statements.

Az eszközárazás második alaptétele (The second fundamental theorem of asset pricing)

A dolgozatban röviden bemutatjuk az eszközárazás második alaptételét. A bizonyítás során felhasználjuk a Dalang-Morton-Wilinger tétel bizonyításában használt állításokat. ______ In the article we summarize the results about the second fundamental theorem of asset pricing.

Off-equilibrium fluctuation-dissipation relations in the 3d Ising spin glass in a magnetic field

We study the fluctuation-dissipation relations for a three dimensional Ising spin glass in a magnetic field both in the high temperature phase as well as in the low temperature one. In the region of times simulated we have found that our results support a picture of the low temperature phase with broken replica symmetry, but a droplet behavior cannot be completely excluded.

Centralizers of normal subgroups and the Z*-theorem

Peer reviewed

Centralizers of normal subgroups and the Z*-theorem

Peer reviewed

Centralizers of normal subgroups and the Z*-theorem

Peer reviewed

Ground and Electronic Excited States from Pairing Matrix Fluctuation and Particle-Particle Random Phase Approximation

The accurate description of ground and electronic excited states is an important and challenging topic in quantum chemistry. The pairing matrix fluctuation, as a counterpart of the density fluctuation, is applied to this topic. From the pairing matrix fluctuation, the exact electron correlation energy as well as two electron addition/removal energies can be extracted. Therefore, both ground state and excited states energies can be obtained and they are in principle exact with a complete knowledge of the pairing matrix fluctuation. In practice, considering the exact pairing matrix fluctuation is unknown, we adopt its simple approximation --- the particle-particle random phase approximation (pp-RPA) --- for ground and excited states calculations. The algorithms for accelerating the pp-RPA calculation, including spin separation, spin adaptation, as well as an iterative Davidson method, are developed. For ground states correlation descriptions, the results obtained from pp-RPA are usually comparable to and can be more accurate than those from traditional particle-hole random phase approximation (ph-RPA). For excited states, the pp-RPA is able to describe double, Rydberg, and charge transfer excitations, which are challenging for conventional time-dependent density functional theory (TDDFT). Although the pp-RPA intrinsically cannot describe those excitations excited from the orbitals below the highest occupied molecular orbital (HOMO), its performances on those single excitations that can be captured are comparable to TDDFT. The pp-RPA for excitation calculation is further applied to challenging diradical problems and is used to unveil the nature of the ground and electronic excited states of higher acenes. The pp-RPA and the corresponding Tamm-Dancoff approximation (pp-TDA) are also applied to conical intersections, an important concept in nonadiabatic dynamics. Their good description of the double-cone feature of conical intersections is in sharp contrast to the failure of TDDFT. All in all, the pairing matrix fluctuation opens up new channel of thinking for quantum chemistry, and the pp-RPA is a promising method in describing ground and electronic excited states.

Does estrogen fluctuation throughout the menstrual cycle impact flow-mediated dilation during exercise in healthy premenopausal women?

The endothelium is the inner most layer of cells that lines all arteries. A primary function of endothelial cells is to regulate responses to increased blood flow and the resulting frictional forces or shear stress by producing factors such as nitric oxide that mediate arterial dilation (flow mediated dilation (FMD)). Menstrual cycle variations in estrogen (E2) have been shown to influence brachial artery (BA) FMD in response to transient increases in shear stress brought about by the release of a brief forearm occlusion (reactive hyperemia (RH)). FMD can also be assessed in response to a sustained shear stress stimulus such as that created with handgrip exercise (HGEX), and studies have shown that RH- and HGEX stimulated FMD provide unique information regarding endothelial function. However, the impact of menstrual phase on HGEX-FMD is unknown. Therefore, the purpose of this study was to determine the impact of cyclical changes in E2 levels on HGEX-FMD over two discrete phases of the menstrual cycle. FMD was assessed via ultrasound. 12 subjects (21 ± 2yrs) completed two experimental visits: (1) low estrogen phase (early follicular) and (2) High estrogen phase (late follicular). In each visit both RH- and HGEX-FMD (6 min handgrip exercise) were assessed. Results are mean ± SD. E2 increased from the low to the high estrogen phase of the menstrual cycle (low: 34 ± 8, high: 161 ± 113pg/mL, p = 0.004). There was no change in mean FMD between phases (RH-FMD: 7.7 ± 4.3% vs. 6.4 ± 3.1%, p = 0.139; HGEX-FMD: 4.8 ± 2.8% vs. 4.8 ± 2.3%, p = 0.979). The observation that both RH- and HGEX-FMD did not differ between phases indicates that menstrual cycle fluctuations in estrogen may not universally impact endothelial function in young, healthy premenopausal women. Further research is needed to improve our understanding of the mechanisms that underlie variability in the impact of menstrual phase on both transient and sustained FMD responses.