Generalized Fock spaces and the Stirling numbers

The Bargmann-Fock-Segal space plays an important role in mathematical physics, and has been extended into a number of directions. In the present paper we imbed this space into a Gelfand triple. The spaces forming the Fr\'echet part (i.e. the space of test functions) of the triple are characterized both in a geometric way and in terms of the adjoint of multiplication by the complex variable, using the Stirling numbers of the second kind. The dual of the space of test functions has a topological algebra structure, of the kind introduced and studied by the first named author and G. Salomon.Comment: revised versio

Series expansions for the third incomplete elliptic integral via partial fraction decompositions

We find convergent double series expansions for Legendre's third incomplete elliptic integral valid in overlapping subdomains of the unit square. Truncated expansions provide asymptotic approximations in the neighbourhood of the logarithmic singularity $(1,1)$ if one of the variables approaches this point faster than the other. Each approximation is accompanied by an error bound. For a curve with an arbitrary slope at $(1,1)$ our expansions can be rearranged into asymptotic expansions depending on a point on the curve. For reader's convenience we give some numeric examples and explicit expressions for low-order approximations.Comment: The paper has been substantially updated (hopefully improved) and divided in two parts. This part is about third incomplete elliptic integral. 10 page

Quantum symmetries and exceptional collections

We study the interplay between discrete quantum symmetries at certain points in the moduli space of Calabi-Yau compactifications, and the associated identities that the geometric realization of D-brane monodromies must satisfy. We show that in a wide class of examples, both local and compact, the monodromy identities in question always follow from a single mathematical statement. One of the simplest examples is the Z_5 symmetry at the Gepner point of the quintic, and the associated D-brane monodromy identity

A millimeter-wave tunneLadder TWT

A millimeter wave traveling wave tube was developed using a dispersive, high impedance forward interaction structure based on a ladder, with non-space harmonic interaction, for a tube with high gain per unit length and high efficiency. The TunneLadder interaction structure combines ladder properties modified to accommodate Pierce gun beam optics in a radially magnetized permanent magnet focusing structure. The development involved the fabrication of chemically milled, shaped ladders diffusion brazed to diamond cubes which are in turn active-diffusion brazed to each ridge of a doubly ridged waveguide. Cold test data are presented, representing the omega-beta and impedance characteristics of the modified ladder circuit. These results were used in small and large signal computer programs to predict TWT gain and efficiency. Actual data from tested tubes verify the predicted performance while providing broader bandwidth than expected

Government-Industry Cooperative Fisheries Research in the North Pacific under the MSFCMA

The National Marine Fisheries Service’s Alaska Fisheries Science Center (AFSC) has a long and successful history of conducting research in cooperation with the fishing industry. Many of the AFSC’s annual resource assessment surveys are carried out aboard chartered commercial vessels and the skill and experience of captains and crew are integral to the success of this work. Fishing companies have been contracted to provide vessels and expertise for many different types of research, including testing and evaluation of survey and commercial fishing gear and development of improved methods for estimating commercial catch quantity and composition. AFSC scientists have also participated in a number of industry-initiated research projects including development of selective fishing gears for bycatch reduction and evaluating and improving observer catch composition sampling. In this paper, we describe the legal and regulatory provisions for these types of cooperative work and present examples to illustrate the process and identify the requirements for successful cooperative research

Statistical Mechanics of Steiner trees

The Minimum Weight Steiner Tree (MST) is an important combinatorial optimization problem over networks that has applications in a wide range of fields. Here we discuss a general technique to translate the imposed global connectivity constrain into many local ones that can be analyzed with cavity equation techniques. This approach leads to a new optimization algorithm for MST and allows to analyze the statistical mechanics properties of MST on random graphs of various types

The solution of a mixed boundary value problem in the theory of diffraction by a semi-infinite plane

A solution is obtained for the problem of the diffraction of a plane wave sound source by a semi-infinite half plane. One surface of the half plane has a soft (pressure release) boundary condition, and the other surface a rigid boundary condition. Two unusual features arise in this boundary value problem. The first is the edge field singularity. It is found to be more singular than that associated with either a completely rigid or a completely soft semi-infinite half plane. The second is that the normal Wiener-Hopf method (which is the standard technique to solve half plane problems) has to be modified to give the solution to the present mixed boundary value problem. The mathematical problem which is solved is an approximate model for a rigid noise barrier, one face of which is treated with an absorbing lining. It is shown that the optimum attenuation in the shadow region is obtained when the absorbing lining is on the side of the screen which makes the smallest angle to the source or the receiver from the edge

Approximately coloring graphs without long induced paths

It is an open problem whether the 3-coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on $t$ vertices, for fixed $t$. We propose an algorithm that, given a 3-colorable graph without an induced path on $t$ vertices, computes a coloring with $\max\{5,2\lceil{\frac{t-1}{2}}\rceil-2\}$ many colors. If the input graph is triangle-free, we only need $\max\{4,\lceil{\frac{t-1}{2}}\rceil+1\}$ many colors. The running time of our algorithm is $O((3^{t-2}+t^2)m+n)$ if the input graph has $n$ vertices and $m$ edges