Lotka--Volterra Type Equations and their Explicit Integration

In the present note we give an explicit integration of some two--dimensionalised Lotka--Volterra type equations associated with simple Lie algebras, other than the familiar $A_n$ case, possessing a representation without branching. This allows us, in particular, to treat the first fundamental representations of $A_r$, $B_r$, $C_r$, and $G_2$ on the same footing.Comment: 3 pages LATEX fil

Four-dimensional BPS-spectra via M-theory

We consider the realization of four-dimensional theories with N = 2 supersymmetry as M-theory configurations including a five-brane. Our emphasis is on the spectrum of massive states, that are realized as two-branes ending on the five-brane. We start with a determination of the supersymmetries that are left unbroken by the background metric and five-brane. We then show how the central charge of the N = 2 algebra arises from the central charge associated with the M-theory two-brane. This determines the condition for a two-brane configuration to be BPS-saturated in the four-dimensional sense. By imposing certain conditions on the moduli, we can give concrete examples of such two-branes. This leads us to conjecture that vectormultiplet and hypermultiplet BPS-saturated states correspond to two-branes with the topology of a cylinder and a disc respectively. We also discuss the phenomenon of marginal stability of BPS-saturated states.Comment: 18 pages, 3 figures, uses harvmac. References adde

Synthesis of Schiff bases derived from 2-hydroxy-1- naphth- aldehyde and their tin(II) complexes for antimicribial and antioxidant activities

The current studies were designed to prepare tin(II) complexes of various Schiff base derivatives of 2-hydroxy-1-naphthaldehyde (HN) with L-histidine and sulfamethazine have been prepared and characterized by different physiochemical studies such as elemental analysis, atomic absorption, UV-Vis spectra, FTIR spectra, 1H–NMR, 13C-NMR and conductance studies. Antimicrobial and antioxidant activities were also calculated. Antibacterial activity was evaluated by the agar-well diffusion method. Two Gram-negative (Klebsiella pneumoniae and Escherichia coli) and three Gram-positive (Staphylococcus aureus, Staphylococcus epidermidis and Bacillus subtilis) bacterial strains were used. Antifungal activity was resolute against three fungal strains (Aspergillus niger, Aspergillus flavus and Alternaria solani) by using the agar tube dilution method. The antioxidant activity of ligands and their complexes was measured on the basis of the radical scavenging effect of 1,1-diphenyl-2-picryl-hydrazyl (DPPH)-free radical activity. Ligand HNSM exhibited excellent activities as antibacterial activity (22 mm), antifungal activity (55%) and antioxidant activity (119 ppm).               KEY WORDS: Schiff base, 2-Hydroxy-1-naphthaldehyde, L-Histidine and sulfamethazine, Tin(II) complexes, Antimicrobial activities, Antioxidant activities Bull. Chem. Soc. Ethiop. 2017, 31(3), 445-456. DOI: http://dx.doi.org/10.4314/bcse.v31i3.

Period Integrals, Quantum Numbers and Confinement in SUSY QCD

We present a direct computation of the period integrals on degenerate Seiberg-Witten curves for supersymmetric QCD, and show how these periods determine the changes in the quantum numbers of the states, when passing from the weak to the strong-coupling domains in the mass moduli space of the theory. The confinement of monopoles at strong coupling is discussed, and we demonstrate that the ambiguities in choosing the way in the moduli space do not influence to the physical conclusions on confinement of monopoles in the phase with the condensed light dyons.Comment: 16 pages, contribution to special volume on Integrable Systems in Quantum Theor

Vacuum structure of spontaneously broken N=2 supersymmetric gauge theory

We analyze the vacuum structure of spontaneously broken N=2 supersymmetric gauge theory with the Fayet-Iliopoulos term. Our theory is based on the gauge group SU(2) \times U(1) with N_f=1,2 massless quark hypermultiplets having the same U(1) charges. In the classical potential, there are degenerate vacua even in the absence of supersymmetry. It is shown that this vacuum degeneracy is smoothed out, once quantum corrections are taken into account. In N_f=1 case, the effective potential is found to be so-called runaway type, and there is neither well-defined vacuum nor local minimum. On the other hand, in N_f=2 case, while there is also the runaway direction in the effective potential, we find the possibility that there appears the local minimum with broken supersymmetry at the degenerate dyon point.Comment: 27 pages, revtex, 14 figures, some typographical errors are corrected. To be published in Phys. Rev.

Quantum Wall Crossing in N=2 Gauge Theories

We study refined and motivic wall-crossing formulas in N=2 supersymmetric gauge theories with SU(2) gauge group and N_f < 4 matter hypermultiplets in the fundamental representation. Such gauge theories provide an excellent testing ground for the conjecture that "refined = motivic."Comment: 24 pages, 4 figure

Encoding One Logical Qubit Into Six Physical Qubits

We discuss two methods to encode one qubit into six physical qubits. Each of our two examples corrects an arbitrary single-qubit error. Our first example is a degenerate six-qubit quantum error-correcting code. We explicitly provide the stabilizer generators, encoding circuit, codewords, logical Pauli operators, and logical CNOT operator for this code. We also show how to convert this code into a non-trivial subsystem code that saturates the subsystem Singleton bound. We then prove that a six-qubit code without entanglement assistance cannot simultaneously possess a Calderbank-Shor-Steane (CSS) stabilizer and correct an arbitrary single-qubit error. A corollary of this result is that the Steane seven-qubit code is the smallest single-error correcting CSS code. Our second example is the construction of a non-degenerate six-qubit CSS entanglement-assisted code. This code uses one bit of entanglement (an ebit) shared between the sender and the receiver and corrects an arbitrary single-qubit error. The code we obtain is globally equivalent to the Steane seven-qubit code and thus corrects an arbitrary error on the receiver's half of the ebit as well. We prove that this code is the smallest code with a CSS structure that uses only one ebit and corrects an arbitrary single-qubit error on the sender's side. We discuss the advantages and disadvantages for each of the two codes.Comment: 13 pages, 3 figures, 4 table

Type IIB Matrix Theory at Two Loops

The IKKT matrix model was proposed to be a non-perturbative formulation of type IIB superstring theory. One of its important consistency criteria is that the leading one-loop $1/r^8$ effective interaction between a cluster of type IIB D-objects should not receive any corrections from higher loop effects for it to describe accurately the type IIB supergravity results. In analogy with the BFSS matrix model {\it versus} the eleven-dimensional supergravity example, we show in this work that the one-loop effective potential in the IKKT matrix model is also not renormalized at the two-loop order.Comment: 19 pages, Latex, corrected some typos and 1 figure adde