Existence of self-similar blow-up solutions for Zakhrov equation in dimension two. Part I

We consider the Zakharov equation in space dimension two

Concentration properties of blow-up solutions and instability results for Zakharov equation in dimension two. Part II

We consider the Zakharov equation in space dimension two

Green's functions in broken discrete symmetry

Scalar fields with interaction

The equation of motion and gravitational radiation of a small extended spherically symmetric mass

On the basis of an approximation method developed in a previous paper the motion of an extended small mass on a gravitational background is investigated. The mass is described by a spherically symmetric rest mass distribution with some form of rigidity; the smallness of the mass is defined by the assumption that the radius of the mass is small compared with the change of the background . The equation of motion is yielded by integrating Einstein's conservation law of energy and momentum over the world tube of the mass. In the lowest mixed order (mixed of the background and the retarded potentials of the mass in lowest order) this equation is identical with the geodesic line linearized in . In the case when the motion on a static background generated by a localized matter distribution is finite, the gravitational radiation of the mass in lowest order is given.     

A remark on tensor representations

The identity $$\sum\limits_{v = 0} {\left( {\begin{array}{*{20}c} {n + 1} \\ v \\ \end{array} } \right)\left[ {\left( {\begin{array}{*{20}c} {n - v} \\ v \\ \end{array} } \right) - \left( {\begin{array}{*{20}c} {n - v} \\ {v - 1} \\ \end{array} } \right)} \right] = ( - 1)^n } $$ is proved and, by means of it, the coefficients of the decomposition ofD ₁ ⁿ into irreducible representations are found. It holds: ifD ₁ ⁿ \(\mathop {\sum ^n }\limits_{m = 0} A_{nm} D_m \) , then $$A_{nm} = \mathop \sum \limits_{\lambda = 0} \left( {\begin{array}{*{20}c} n \\ \lambda \\ \end{array} } \right)\left[ {\left( {\begin{array}{*{20}c} \lambda \\ {n - m - \lambda } \\ \end{array} } \right) - \left( {\begin{array}{*{20}c} \lambda \\ {n - m - \lambda - 1} \\ \end{array} } \right)} \right].$$      

Regularity of weak solutions to a two-dimensional modified Dirac-Klein-Gordon system of equations

We show that solutions to the modified Dirac-Klein-Gordon system in standard notation

Simultaneous geometrization of classical and quantum mechanics of spinless particles

It is shown that classical and quantum equations of motion of a relativistic spinless particle (the Lorentz and Klein-Gordon equations) allow for a geometrization on the same manifold ₄. A classical particle on ₄ is described as a free particle ( p=0), while the quantum particle, as a free wave ( s=0).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 70–74, September, 1990.     

The equation of motion and gravitational radiation of an ideal fluid sphere moving in a gravitational background

On the basis of an approximation method developed in a previous paper the motion of an ideal fluid sphere in a weak gravitational background is investigated. The sphere is assumed to be small in the sense that its radius is small compared with the change of the background . Furthermore the deformations of the sphere when accelerated by the background are assumed to be small compared with the extension of the sphere in the absence of acceleration. In the lowest mixed order (mixed of the background and the retarded potentials of the sphere in lowest order) the equation of motion is yielded by integrating Einstein's conservation law of energy and momentum over the world-tube of the sphere. One obtains an equation of motion for the center of the sphere that is identical with the geodesic line linearized in . In the case of a static background of a localized matter distribution it is shown that Einstein's energy-momentum complex formed with the retarded potentials from the accelerated motion of the sphere in lowest order (lowest mixed order) leads to an outgoing radiation of gravitational energy. All radiation terms can be expressed in terms of the background and the world-line of the center of the sphere.     

Generalized parton distributions in impact parameter space

The kinematical factor in the positivity bound (36) is incorrect. The bound correctly reads Our corrected result agrees with inequality (25) in [1], taking into account the different normalization conventions here and there.Published online: 9 October 2003Erratum published online: 10 October 2003     

A nonlinear instability for 3×3 systems of conservation laws

The phenomenon of nonlinear resonance provides a mechanism for the unbounded amplification of small solutions of systems of conservation laws. We construct spatially 2-periodic solutionsu ^N C ([0,t _N ] × witht _N bounded, satisfying

A study of conformationl transformations in guttapercha by infrared spectroscopy

The infrared spectra of crystalline - and -guttapercha, and also of molten guttapercha, were studied in the 400–1700 cm^–1 range. It is shown that the IR spectra of the two crystalline modifications exhibit marked differences. The absorption bands characterizing the crystalline - and -forms were determined. The crystalline bands were used to determine the melting points of the two forms. It is shown that stretching of the -form produces a more elongated rotational isomer, i. e., guttapercha; the -form is produced by recrystallization of the -form. The dichroism of the C=C valence vibrations observed in the spectrum of oriented guttapercha indicated that the molecular chains of the -form have a spiral conformation. Guttapercha, i. e., trans-polyisoprene exists in crystalline form at room temperature.     

Determinants,finite-difference operators and boundary value problems

We relate the determinants of differential and difference operators to the boundary values of solutions of the operators. Previous proofs of related results have involved considering one-parameter families of such operators, showing the desired quantities are equal up to a constant, and then calculating the constant. We take a more direct approach. For a fixed operator, we prove immediately that the two sides of our formulas are equal by using the following simple observation (Proposition 1.3):Let USU(n,C).Write U in block form

Levinson's Theorem for the Nonlocal Interaction in One Dimension

The Levinson theorem for the one-dimensional Schrödinger equation with both local and the nonlocal symmetric potentials is established by the Sturm–Liouville theorem. The critical case where the Schro;audinger equation has a finite zero-energy solution is also analyzed. It is shown that the number n ₊ (n _–) of bound states with even (odd) parity is related to the phase shift ₊(0)[_–(0)] of the scattering states with the same parity at zero momentum as

Unitary dressing transformations and exponential decay below threshold for quantum spin systems. Parts III and IV

This is the continuation of a series of articles concerning a class of quantum spin systems with Hamiltonian operators of the form

Decomposition of Higher-Order Equations of Monge–Ampère Type

It is demonstrated that the fourth-order PDE

Updated estimate of the muon magnetic momentusing revised results from <Emphasis Type="Italic">e</Emphasis><Superscript> + </Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>-</Superscript>annihilation

A new evaluation of the hadronic vacuum polarization contribution to the muon magnetic moment is presented. We take into account the reanalysis of the low-energy e ⁺ e ^-annihilation cross section into hadrons by the CMD-2 Collaboration. The agreement between e ⁺ e ^-and spectral functions in the channel is found to be much improved. Nevertheless, significant discrepancies remain in the center-of-mass energy range between 0.85 and , so that we refrain from averaging the two data sets. The values found for the lowest-order hadronic vacuum polarization contributions are where the errors have been separated according to their sources: experimental, missing radiative corrections in e ⁺ e ^-data, and isospin breaking. The corresponding Standard Model predictions for the muon magnetic anomaly read where the errors account for the hadronic, light-by-light (LBL) scattering and electroweak contributions. The deviations from the measurement at BNL are found to be (1.9 ) and (0.7 ) for the e ⁺ e ^-- and -based estimates, respectively, where the second error is from the LBL contribution and the third one from the BNL measurement.Received: 7 September 2003, Published online: 30 October 2003     

A measurement of the forward-backward asymmetry of e+e?→bb by applying a jet charge algorithm to lifetime tagged events

The forward-backward asymmetry of has been measured using approximately 2.15 million hadronicZ ⁰ decays collected at the LEP e⁺e^– collider with the OPAL detector. A lifetime tag technique was used to select an enriched event sample. The measurement of the asymmetry was then performed using a jet charge algorithm to determine the direction of the primary quark. Values of:

Nonpersistence of breather families for the perturbed sine Gordon equation

We show that, up to one exception and as a consequence of first order perturbation theory only, it is impossible that a large portion of the well-known family of breather solutions to the sine Gordon equation could persist under any nontrivial perturbation of the form

Long-Time Asymptotics of Solutions to the Cauchy Problem for the Defocusing Nonlinear Schrödinger Equation with Finite-Density Initial Data. II. Dark Solitons on Continua

For Lax-pair isospectral deformations whose associated spectrum, for given initial data, consists of the disjoint union of a finitely denumerable discrete spectrum (solitons) and a continuous spectrum (continuum), the matrix Riemann–Hilbert problem approach is used to derive the leading-order asymptotics as of solutions to the Cauchy problem for the defocusing nonlinear Schrödinger equation ( NLSE), , with finite-density initial data

Superconductive superheating field for finiteκ

We have calculated analytically the superheating fieldH _sh for bulk superconductors, correct to second order in. We find , which agrees well with numerical computations for<0.5. The surface order parameter is , and the penetration depth is .