Moments of an exponential functional of random walks and permutations with given descent sets

The exponential functional of simple, symmetric random walks with negative drift is an infinite polynomial Y = 1 + ξ₁ + ξ₁ξ₂ + ξ₁ξ₂ξ₃ + ⋯ of independent and identically distributed non-negative random variables. It has moments that are rational functions of the variables μ _k = E(ξ ^k ) < 1 with universal coefficients. It turns out that such a coefficient is equal to the number of permutations with descent set defined by the multiindex of the coefficient. A recursion enumerates all numbers of permutations with given descent sets in the form of a Pascal-type triangle. This revised version was published online in August 2006 with corrections to the Cover Date.     

Copper-facilitated Suzuki-Miyaura coupling for the preparation of 1,3-dioxolane-protected 5-arylthiophene-2-carboxaldehydes

5-Formyl-2-thiopheneboronic acid is a widely used building block for the synthesis of diverse structures, however, due to a significant instability its transformation to 5-arylthiophene-2-carboxaldehydes by CC couplings could be performed only in low yields. Herein, as a solution, a convenient technique is described for the preparation of 1,3-dioxolane-protected 5-arylthiophene-2-carboxaldehydes via a one-pot borylation–copper(I) chloride co-catalyzed Suzuki-Miyaura coupling reaction. The utilization of the in situ prepared 2-thiopheneboronic ester derivative is allowed by the method developed. Elimination of the crucial, acidic liberation step of boronic acid species resulted in improved yields and purities. In addition, comparison of various aryl bromides is shown to demonstrate the high tolerance of the transformation to functional groups.     

Influence of oxidative injury and monitoring of blood plasma by DSC on breast cancer patients

Damage caused by oxidative stress is involved in many types of diseases, including breast cancer. Our aim was to detect the oxidative stress parameters and blood plasma changes with differential scanning calorimetry (DSC) in breast cancer patients. The study included 40 adult breast cancer women who were grouped according to tumor diameter, regional lymph node metastases, proliferative activity, receptor status and postoperative chemotherapy. To monitor oxidative stress, malondialdehyde, oxygen free radicals (OFRs), activity of myeloperoxidase (MPO), superoxide dismutase (SOD) and catalase (CAT) were measured. Denaturation of plasma components was detected in Setaram Micro DSC-II calorimeter. The total production of OFRs, the MPO activity and lipidperoxidation were significantly increased in each breast cancer patients considering the tumor size, the metastatic lymph nodes, the proliferation activity and receptor status compared with healthy controls (p < 0.05). These pro-oxidants were slightly elevated without chemotherapy, but their values were increased significantly in chemotherapy-receiving group. The activity of SOD and CAT was significantly decreased in all groups, and in regard to the chemotherapy, they were changed significantly parallel to the severity of disease. Regarding to both the increased tumor diameter and the increased number of affected lymph nodes, DSC measurements showed a strong relationship between the maximum excess heat capacity (C_pmax) of the blood plasma and the severity of disease. The study demonstrated that oxidative stress is implicated in breast carcinoma and chemotherapy aggravates these changes which confirmed the plasma DSC measurements also.     

Nonlinear optical characteristics of monolayer MoSe2

In this study, we utilized picosecond pulses from an Nd:YAG laser to investigate the nonlinear optical characteristics of monolayer MoSe₂. Two‐step growth involving the selenization of pulsed‐laser‐deposited MoO₃ film was employed to yield the MoSe₂ monolayer on a SiO₂/Si substrate. Raman scattering, photoluminescence (PL) spectroscopy, and atomic force microscopy verified the high optical quality of the monolayer. The second‐order susceptibility χ⁽²⁾ was calculated to be ～50 pm V^?1 at the second harmonic wavelength ～810 nm, which is near the optical gap of the monolayer. Interestingly, our wavelength‐dependent second harmonic scan can identify the bound excitonic states including negatively charged excitons much more efficiently, compared with the PL method at room temperature. Additionally, the MoSe₂ monolayer exhibits a strong laser‐induced damage threshold ～16 GW cm^?2 under picosecond‐pulse excitation_. Our findings suggest that monolayer MoSe₂ can be considered as a promising candidate for high‐power, thin‐film‐based nonlinear optical devices and applications.     

On the semiring of cone preserving maps

If K is a proper cone in Rⁿ, then the cone of all linear operators that preserve K, denoted by π(K), forms a semiring under usual operator addition and multiplication. Recently J.G. Horne examined the ideals of this semiring. He proved that if K₁, K₂ are polyhedral cones such that π(K₁) and π(K₂) are isomorphic as semirings, then K₁ and K₂ are linearly isomorphic. The study of this semiring is continued in this paper. In Sec. 3 ideals of π(K) which are also faces are characterized. In Sec. 4 it is shown that π(K) has a unique minimal two-sided ideal, namely, the dual cone of π(K¹), where K¹ is the dual cone of K. Extending Horne's result, it is also proved that the cone K is characterized by this unique minimal two-sided ideal of π(K). The set of all faces of π(K) inherits a quotient semiring structure from π(K). Properties of this face-semiring are given in Sec. 5. In particular, it is proved that this face-semiring admits no nontrivial congruence relation iff the duality operator of π(K) is injective. In Sec. 6 the maximal one-sided and two-sided ideals of π(K) are identified. In Sec. 8 it is shown that π(K) never satisfies the ascending-chain condition on principal one-sided ideals. Some partial results on the question of topological closedness of principal one-sided ideals of π(K) are also given.     

Kinetische Untersuchung der basenkatalysierten Chalkonbildung

Zusammenfassung Es wurde die mit Benzaldehyd, 4-Chlor- und 4-Nitrobenzaldehyd in Gegenwart von Natriumhydroxyd ablaufende Kondensation des 5-Nitro-2-hydroxy-acetophenons kinetisch untersucht. Dabei stellte sich heraus, daß die Reaktion reversibel und ferner ihre Teilordnung für alle drei Komponenten 1 ist. Die an dem p-C-Atom zur Aldehydkomponente stehenden elektronenanziehenden Substituenten bewirken Steigerung der Reaktionsgeschwindigkeit und beeinflussen die Werte der Gleichgewichtskonstante und der Aktivierungsenergie.Mit 8 Abbildungen     

Continuity of the Solution Map in Parametric Affine Variational Inequalities

A systematic study of the upper semicontinuity and the lower semicontinuity of the solution map in parametric affine variational inequalities is given in this paper. Several examples are constructed to analyze the results. This work was supported by Korea Research Foundation Grant (KRF 2001-015-DP0049), the APEC Postdoctoral Fellowships Program, and the KOSEF Brain Pool Program.