Iminobis(Methylenediphosphonic) acid

Conclusions When formamide was reacted with phosphorous acid and phosphorus trichloride, the formation of iminobis(methylenediphosphonic) acid was detected.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 4, pp. 865–868, April, 1987.The authors wish to express their graditude to Yu. P. Tsentalovich for helping with the NMR spectral analysis.     

Poincaré’s inequalities and Talagrand’s concentration phenomenon for the exponential distribution

Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper bounds on spectral gaps. Received: 10 June 1996 / In revised form: 9 August 1996     

On Concentration of Empirical Measures and Convergence to the Semi-circle Law

Concentration properties of the general empirical distribution functions and the rate of convergence of spectral empirical distributions to the semi-circle law in the case of symmetric high-dimensional random matrices are studied under Poincaré-type inequalities.     

Zero-energy Andreev surface bound states in the lattice model

The conditions for zero-energy Andreev surface bound states to exist are found for the lattice model of a d-wave superconductor with arbitrary surface orientation. Both nearest-neighbors and next-nearest-neighbors models are considered. It is shown that the results are very sensitive to the surface orientation. In particular, for a half-filled (hl0)-surface, zero-energy Andreev surface states only appear under the condition that h and l are odd simultaneously.     

Reaction of pyrophosphites with carboxylate esters

Conclusions Reaction of formates with tetraalkyl pyrophosphites in the presence of boron trifluoride gives alkoxy(aryloxy)methylenediphosphonic acids.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 2, pp. 630–633, February, 1987.     

SIMS study of the processes in buffer solutions of bioorganic systems

Enzymatic glucose oxidation in a system modeling a glucose biosensor have been investigated by SIMS with the use of a liquid matrix. The effect of some solution parameters on the reaction product (gluconic acid) yield has been analyzed. It is shown by an example of gluconolactone hydrolysis that SIMS makes it possible to study not only final but also intermediate stage of the glucose oxidation reaction.     

Reaction of 8-bromotheophylline with pyridine and alkylpyridines. 8-Pyridiniotheophyllinates

The reaction of 8-bromotheophylline with pyridine or alkylpyridines in the presence of electrophilic reagents proceeds with the formation of 8-pyridiniotheophyllinates. The possible mechanism of the reaction is discussed.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1541–1544, November, 1990.     

Dimensional behaviour of entropy and information

We develop an information-theoretic perspective on some questions in convex geometry, providing for instance a new equipartition property for log-concave probability measures, some Gaussian comparison results for log-concave measures, an entropic formulation of the hyperplane conjecture, and a new reverse entropy power inequality for log-concave measures analogous to V. Milman's reverse Brunn–Minkowski inequality.     

A Strong Maximum Principle for parabolic equations with the p-Laplacian

We prove the Strong Maximum Principle (SMP) under suitable assumptions for a class of quasilinear parabolic problems with the p  -Laplacian, p>1$p>1$, on bounded cylindrical domains of R^N+1${\mathbb{R}}^{N+1}$,

_∂tu−_Δpu−λ|u|^p−2u≥0,${\partial }_{t}u-{\mathrm{\Delta }}_{p}u-\lambda {|u|}^{p-2}u\ge 0,$

with nonnegative initial–boundary conditions and λ≤0$\lambda \le 0$, and we give some counterexamples to the SMP if some of our assumptions are violated. We show that the Hopf Maximum Principle holds for 1<p<2$1<p<2$, and give a counterexample to it for p>2$p>2$. Also the Weak Maximum Principle for λ≤_λ1$\lambda \le {\lambda }_1$ is established.     

On the existence of a continuous branch of nodal solutions of elliptic equations with convex-concave nonlinearities

We study the existence of nodal solutions of a parametrized family of Dirichlet boundary value problems for elliptic equations with convex-concave nonlinearities. In the main result, we prove the existence of nodal solutions u _λ for λ ∈ (?∞, λ*₀). The critical value λ*₀ >0 is found by a spectral analysis procedure according to Pokhozhaev’s fibering method. We show that the obtained solutions form a continuous branch (in the sense of level lines of the energy functional) with respect to the parameter λ. Moreover, we prove the existence of an interval \(( - \infty ,\tilde \lambda )\) , where \(\tilde \lambda > 0\) , on which this branch consists of solutions with exactly two nodal domains.