An Inverse Problem for a Model of a Hierarchical Structure

We consider the inverse problem for the identification of the coefficient in a parabolic equation. The model is applied to describe the functioning of a hierarchical structure [1]; it is also relevant for heat-conduction theory [2]. Unique solvability of the inverse problem is proved.     

Approximate solution of the Cauchy problem for a hyperbolic equation with a nonlinear source

An approximate method is described for the Cauchy problem for a nonlinear hyperbolic equation. The method reduces the problem to an integro-differential equation of 2nd kind that can be solved iteratively. Minimum smoothness conditions are imposed on the nonlinear coefficient. Unique solvability is proved. __________ Translated from Prikladnaya Matematika i Informatika, No. 19, pp. 41–55, 2004.     

MINCRYST: A crystallographic database for minerals, local and network (WWW) versions

MINCRYST is an original interrelated combination of the Crystal Structure Database for Minerals, Subbase of Calculated Polycrystal Standards (Calculated Powder X-ray Diffraction Standard Subbase, CPDS Subbase), and the Applied Program Package. The Information fund of the Crystal Structure Database comprises about 4800 files. Two MINCRYST versions are developed—the local (L) version with the original Database Management System designed for use on a personal computer and the WWW version with an original interface integrated into the WWW server of the Institute of Experimental Mineralogy of the Russian Academy of Sciences (Chernogolovka) accessible to all the Internet users.     

The Inverse Problem for Numerical Determination of the Nonlinear Right-Hand Side in a Parabolic Equation

The article considers the inverse problem of determining the nonlinear right-hand side of a quasi-linear parabolic equation and proves a uniqueness theorem. A method is proposed for numerical solution of the inverse problem based on parametric representation of the sought coefficient. The inverse problem thus reduces to finding the error-minimizing vector of unknown coefficients of the parametric representation of the sought function.     

Boronated protohaemins: synthesis and in vivo antitumour efficacy

The conjugates of porphyrin macrocycles with boron-containing polyhedra are under investigation as agents for binary treatment strategies of cancer. Aiming at the design of photoactive compounds with low-to-zero dark toxicity, we synthesized a series of carboranyl and monocarbon-carboranyl derivatives of protohaemin IX using the activation of porphyrin carboxylic groups with di-tert-butyl pyrocarbonate or pivaloyl chloride. The water-soluble 1,3,5,8-tetramethyl-2,4-divinyl-6(7)-[2'-(closo-monocarbon-carborane-1'-yl)methoxycarbonylethyl]-7(6)-(2'-carboxyethyl)porphyrin Fe(III) (compound 9) exerted no discernible cytotoxicity for cultured mammalian cells, nor did it cause general toxicity in rats. Importantly, 9 demonstrated dose-dependent activity as a phototoxin in photodynamic therapy of M-1 sarcoma-bearing rats. In animals injected with 20 mg kg(-1) of 9, the tumours shrank by day 3 after one single irradiation of the tumour with red laser light. Between 7 and 14 days post-irradiation, 88.9% of rats were tumour-free; no recurrence of the disease was detectable within at least 90 days. Protohaemin IX alone was without effect, indicating that boronation is important for the phototoxic activity of 9. This is the first study that presents the synthesis and preclinical in vivo efficacy of boronated derivatives of protohaemin as phototoxins. The applicability in photodynamic treatment broadens the therapeutic potential of boronated porphyrins beyond their conventional role as radiosensitizers in boron neutron capture therapy.     

On the Pathomorphological Pattern of the Efficiency of Photodynamic Therapy of Murine Melanoma B16 Using a New Photosensitizer Based on Chlorin e6 Conjugate with a Prostate-Specific Membrane Antigen

Photodynamic therapy (PDT) is an effective treatment for a number of solid malignancies. In this work, the antitumor efficacy of photodynamic therapy for murine B16 melanoma with intravenous administration of a new photosensitizer (PS) based on the chlorin e₆ conjugate with a prostate-specific membrane antigen (PSMA) was studied in vivo. We have previously published the data obtained in the first part of the study: the dynamics of PS accumulation in the tumor and surrounding tissues and the antitumor efficacy of the photodynamic therapy, which was evaluated by the regression parameters and morphological characteristics of the tumors—including by the complete regression of the tumors, the absolute growth rate of the tumors among the mice with continued tumor growth, and an increase in life expectancy compared to the control. The criterion for a complete cure was the absence of signs of tumor recurrence within 90 days after therapy. The conducted studies demonstrated the high efficiency of the new photosensitizer for the photodynamic therapy of B16 melanoma. This article presents a continuation of this work, including histological studies of the zones exposed to laser irradiation on the 21st day after treatment and an assessment of the therapeutic potential of photodynamic therapy for the destruction of tumor cells. Pathological studies in the zones of photodynamic exposure revealed that the effectiveness of the PDT depended on the PS dose and the laser irradiation parameters.