Cohomology ring of the brst operator associated to the sum of two pure spinors

In the study of the Type II superstring, it is useful to consider the BRST complex associated to the sum of two pure spinors. The cohomology of this complex is an infinite-dimensional vector space. It is also a finite-dimensional algebra over the algebra of functions of a single pure spinor. In this paper we study the multiplicative structure. © 2013 World Scientific Publishing Company.

k-Hyponormality and n-Contractivity for Agler-Type Shifts

We consider k-hyponormality and n-contractivity (k, n = 1, 2, ...) as "weak subnormalities" for a Hilbert space operator. It is known that k-hyponormality implies 2k-contractivity; we produce some classes of weighted shifts including a parameter for which membership in a certain n-contractive class is equivalent to k-hyponormality. We consider as well some extensions of these results to operators arising as restrictions of these shifts, or from linear combinations of the Berger measures associated with the shifts.

The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

Root system of singular perturbations of the harmonic oscillator type operators

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.

Automatic Inference of Determinacy and Mutual Exclusion for Logic Programs Using Mode and Type Analyses

We propose an analysis for detecting procedures and goals that are deterministic (i.e., that produce at most one solution at most once),or predicates whose clause tests are mutually exclusive (which implies that at most one of their clauses will succeed) even if they are not deterministic. The analysis takes advantage of the pruning operator in order to improve the detection of mutual exclusion and determinacy. It also supports arithmetic equations and disequations, as well as equations and disequations on terms,for which we give a complete satisfiability testing algorithm, w.r.t. available type information. Information about determinacy can be used for program debugging and optimization, resource consumption and granularity control, abstraction carrying code, etc. We have implemented the analysis and integrated it in the CiaoPP system, which also infers automatically the mode and type information that our analysis takes as input. Experiments performed on this implementation show that the analysis is fairly accurate and efficient.

Inferring determinacy and mutual exclusion in logic programs using mode and type analysis.

We propose an analysis for detecting procedures and goals that are deterministic (i.e., that produce at most one solution at most once), or predicates whose clause tests are mutually exclusive (which implies that at most one of their clauses will succeed) even if they are not deterministic. The analysis takes advantage of the pruning operator in order to improve the detection of mutual exclusion and determinacy. It also supports arithmetic equations and disequations, as well as equations and disequations on terms, for which we give a complete satisfiability testing algorithm, w.r.t. available type information. We have implemented the analysis and integrated it in the CiaoPP system, which also infers automatically the mode and type information that our analysis takes as input. Experiments performed on this implementation show that the analysis is fairly accurate and efficient.

Sampling associated with resolvent-type kernels and lagrange-type interpolation series

In this paper a new class of Kramer kernels is introduced, motivated by the resolvent of a symmetric operator with compact resolvent. The article gives a necessary and sufficient condition to ensure that the associ- ated sampling formula can be expressed as a Lagrange-type interpolation series. Finally, an illustrative example, taken from the Hamburger moment problem theory, is included.

On representations of finite type

Representations of the (infinite) canonical anticommutation relations and the associated operator algebra, the fermion algebra, are studied. A “coupling constant” (in (0,1]) is defined for primary states of “finite type” of that algebra. Primary, faithful states of finite type with arbitrary coupling are constructed and classified. Their physical significance for quantum thermodynamical systems at high temperatures is discussed. The scope of this study is broadened to include a large class of operator algebras sharing some of the structural properties of the fermion algebra.

Binding of purified multiple antibiotic-resistance repressor protein (MarR) to mar operator sequences.

Elevated expression of the marORAB multiple antibiotic-resistance operon enhances the resistance of Escherichia coli to various medically significant antibiotics. Transcription of the operon is repressed in vivo by the marR-encoded protein, MarR, and derepressed by salicylate and certain antibiotics. The possibility that repression results from MarR interacting with the marO operator-promoter region was studied in vitro using purified MarR and a DNA fragment containing marO. MarR formed at least two complexes with marO DNA, bound > 30-fold more tightly to it than to salmon sperm DNA, and protected two separate 21-bp sites within marO from digestion by DNase I. Site I abuts the downstream side of the putative -35 transcription-start signal and includes 4 bp of the -10 signal. Site II begins 13 bp downstream of site I, ending immediately before the first base pair of marR. Site II, approximately 80% homologous to site I, is not required for repression since a site II-deleted mutant (marO133) was repressed in trans by wild-type MarR. The absence of site II did not prevent MarR from complexing with the site I of marO133. Salicylate bound to MarR (Kd approximately 0.5 mM) and weakened the interaction of MarR with sites I and II. Thus, repression of the mar operon, which curbs the antibiotic resistance of E. coli, correlates with the formation of MarR-site I complexes. Salicylate appears to induce the mar operon by binding to MarR and inhibiting complex formation, whereas tetracycline and chloramphenicol, which neither bind MarR nor inhibit complex formation, must induce by an indirect mechanism.

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Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative

2000 Mathematics Subject Classification: 35A15, 44A15, 26A33

Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R

2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63

Generalized Sobolev Spaces of Exponential Type Associated with the Dunkl Operators

2000 Mathematics Subject Classification: 35E45

On Limiting Case of the Stein-Weiss Type Inequality for the B-Riesz Potentials

Mathematics Subject Classification: Primary 42B20, 42B25, 42B35

On Generalized Weyl Fractional q-Integral Operator Involving Generalized Basic Hypergeometric Functions

Mathematics Subject Classification: 33D60, 33D90, 26A33