An constructive proof for the Umemura polynomials for the third Painlev\'e equation

We are concerned with the Umemura polynomials associated with the third Painlev\'e equation. We extend Taneda's method, which was developed for the Yablonskii--Vorob'ev polynomials associated with the second Painlev\'e equation, to give an algebraic proof that the rational functions generated by the nonlinear recurrence relation satisfied by Umemura polynomials are indeed polynomials. Our proof is constructive and gives information about the roots of the Umemura polynomials.Comment: 20 pages, 3 figure

An algebraic proof for the Umemura polynomials for the third Painlevé equation

We are concerned with the Umemura polynomials associated with the third Painlev\'e equation. We extend Taneda's method, which was developed for the Yablonskii-Vorob'ev polynomials associated with the second Painlev\'e equation, to give an algebraic proof that the rational functions generated by the nonlinear recurrence relation satisfied by Umemura polynomials are indeed polynomials

2D Qubit Placement of Quantum Circuits using LONGPATH

In order to achieve speedup over conventional classical computing for finding solution of computationally hard problems, quantum computing was introduced. Quantum algorithms can be simulated in a pseudo quantum environment, but implementation involves realization of quantum circuits through physical synthesis of quantum gates. This requires decomposition of complex quantum gates into a cascade of simple one qubit and two qubit gates. The methodological framework for physical synthesis imposes a constraint regarding placement of operands (qubits) and operators. If physical qubits can be placed on a grid, where each node of the grid represents a qubit then quantum gates can only be operated on adjacent qubits, otherwise SWAP gates must be inserted to convert non-Linear Nearest Neighbor architecture to Linear Nearest Neighbor architecture. Insertion of SWAP gates should be made optimal to reduce cumulative cost of physical implementation. A schedule layout generation is required for placement and routing apriori to actual implementation. In this paper, two algorithms are proposed to optimize the number of SWAP gates in any arbitrary quantum circuit. The first algorithm is intended to start with generation of an interaction graph followed by finding the longest path starting from the node with maximum degree. The second algorithm optimizes the number of SWAP gates between any pair of non-neighbouring qubits. Our proposed approach has a significant reduction in number of SWAP gates in 1D and 2D NTC architecture.Comment: Advanced Computing and Systems for Security, SpringerLink, Volume 1

Poly[(μ6-benzene-1,3,5-tricarboxyl­ato-κ6 O 1:O 1′:O 3:O 3′:O 5:O 5′)tris­(N,N-dimethyl­formamide-κO)tris­(μ3-formato-κ2 O:O′)trimagnesium(II)]

The title complex, [Mg3(CHO2)3(C9H3O6)(C3H7NO)3]n, exhib­its a two-dimensional structure parallel to (001), which is built up from the MgII atoms and bridging carboxyl­ate ligands (3 symmetry). The MgII atom is six-coordinated by one O atom from a dimethyl­formamide mol­ecule, two O atoms from two μ6-benzene-1,3,5-tricarboxyl­ate ligands and three O atoms from three μ3-formate ligands in a distorted octa­hedral geometry

Submandibular Cavernous Hemangiomas with Multiple Phleboliths Masquerading as Sialolithiasis

Vasoformative tumors (almost exclusively hemangiomas) are the most common lesions of the major salivary glands during infancy and early childhood. They are more common in the parotid gland but are particularly rare in the submandibular gland. Changes in blood flow dynamics within hemangiomas result in thrombus formation and phleboliths. Hemangiomas of the salivary glands in adults are histologically unlike those in infants, the former being characteristically of the cavernous variant. Most cavernous hemangiomas require surgery since they do not show a tendency to regress. A case of an adult man with cavernous hemangioma affecting the submandibular salivary gland that clinically simulated sialolithiasis is presented to alert surgeons to the possibility of such a lesion. We describe the clinical course and review the literature