Related papers: New rigid string instantons in $R^4$
A class of first order linear impulsive differential equation with continuous and piecewise constant arguments is studied. Sufficient conditions for the oscillation of the solutions are obtained.
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
A relationship between 4d gauge theory and 2d CFT will be reviewed from the very basics. We will first cover the introductory material on the 2d CFT and on the instantons of 4d gauge theory. Next we will explicitly calculate and check the…
A class of fourth--order neutral type difference equations with quasidifferences and deviating arguments is considered. Our approach is based on studying the considered equation as a system of a four--dimensional difference system. The…
An expression for four-tangle is obtained by examining the negativity fonts present in a four-way partial transpose under local unitary operations. An alternate derivation of three tangle is also given.
The work deals with the existence of solutions of a certain system of quadratic integral equations in H^2(R^d,R^N), d = 2, 3. We demonstrate the existence of a perturbed solution by virtue of a fixed point technique.
The systems of complex analytic second order ordinary differential equations whose solutions close up to become rational curves (after analytic continuation) are characterized by the vanishing of an explicit differential invariant, and turn…
The effective action for string theory which takes into account non-minimal coupling of moduli admits multi-black hole solutions. The euclidean continuation of these solutions can be interpreted as an instanton mediating the splitting and…
It is shown that Einstein-Yang-Mills-dilaton theory has a countable family of static globally regular solutions which are purely magnetic but uncharged. The discrete spectrum of masses of these solutions is bounded from above by the mass of…
A new version of the alternating directions implicit (ADI) iteration for the solution of large-scale Lyapunov equations is introduced. It generalizes the hitherto existing iteration, by incorporating tangential directions in the way they…
We describe a certain "self-similar" family of solutions to the free Schroedinger equation in all dimensions, and derive some consequences of such solutions for two specific problems.
We prove a theorem which add a new member to Rogers-Ramanujan identities. This new member counts partitions with different type of constraints on even and odd parts. Generalizing this theorem, we obtain two family of partition identities of…
We define (in two, equivalent ways) the notion of a rigid stratum of a reductive group. This generalizes the notion of rigid unipotent class.
We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation for which the numerical solutions can be obtained in a fixed number of forward and backward…
According to a recent classification of 6d (1,0) theories within F-theory there are only six "pure" 6d gauge theories which have a UV superconformal fixed point. The corresponding gauge groups are $SU(3),SO(8),F_4,E_6,E_7$, and $E_8$. These…
We briefly review the status of three-family grand unified string models.
We review recent progress on the resolution of gravitational singularities in string theory. The main example is the fundamental string in five dimensions which is singular in the standard supergravity description but regular after taking…
For the linear baryon string model with three massive points (three quarks) connected sequentially by the relativistic strings the initial-boundary value problem is stated and solved in general. This problem implies defining a classical…
The relativistic string with massive ends (the meson model) and four various string baryon models: q-qq, q-q-q, Y and $\Delta$ are considered. In particular, the rotational motions for all these systems are applied to describing the leading…
We give a characterization of all three points in $\mathbb R^4$ with integer coordinates which are at the same Euclidean distance apart. In three dimension the problem is characterized in terms of solutions of the Diophantine equations…