Critical sets of nonlinear Sturm-Liouville operators of Ambrosetti-Prodi type

The critical set C of the operator F:H^2_D([0,pi]) -> L^2([0,pi]) defined by F(u)=-u''+f(u) is studied. Here X:=H^2_D([0,pi]) stands for the set of functions that satisfy the Dirichlet boundary conditions and whose derivatives are in L^2([0,pi]). For generic nonlinearities f, C=\cup C_k decomposes into manifolds of codimension 1 in X. If f''0, the set C_j is shown to be non-empty if, and only if, -j^2 (the j-th eigenvalue of u -> u'') is in the range of f'. The critical components C_k are (topological) hyperplanes.Comment: 6 pages, no figure

RECENT PROGRESS IN FOREST PRODUCTS RESEARCH

EVER since the development of television and the atomic bomb, research is thought by many to be an easy way of reaching an objective with little or no work or expense. Industries formerly not interested in research, have built laboratories and expected profits to double in a year; uninformed executives have expected research to solve million dollar problems on hundred dollar budgets. Research is producing marvelous results in many areas, but time, work and money are required

Wood Technologists* in Industry

The vast majority of forestry college graduates, majoring in wood utilization subjects, seek their livelihood in or through employment with private industry. There are many reasons why these men will always feel that they chose wisely in selecting that branch of forestry. Men of ability will unquestionably derive the greatest possible income in private industry. The opportunities of exercising initiative are unexcelled. Their work will almost invariably be stimulating, requiring maximum diligence and ingenuity

Economic Comparison of Alternatives to Sulfamethazine Use in Pork Production

Sulfamethazinehas been widely used in the production of meat animals. It is effective as a product for treatment as well as prevention of animal disease leading to improved production efficiencies and lower cost meat and meat products. This was true especially in pork production. However, in recent years, use ofsulfamethazine in meat animal production has received a renewed focus. Thisstudy provides an economic analysis ofselected alternatives to the use of sulfamethazine in pork production. Alternatives evaluated were sulfathiazole, oxytetracycline, chlortetracycline, tylosin and lincomycin. Sulfathiazole isshown to be the most cost effective alternative. Production efficiency, production costs, and pork priceswere only slightly impacted when sulfathiazole was substituted for sulfamethazine. Sulfathiazole is followed by lincomycin, then the tetracyclines, and tylosi

Algebro-Geometric Solutions of the Boussinesq Hierarchy

We continue a recently developed systematic approach to the Bousinesq (Bsq) hierarchy and its algebro-geometric solutions. Our formalism includes a recursive construction of Lax pairs and establishes associated Burchnall-Chaundy curves, Baker-Akhiezer functions and Dubrovin-type equations for analogs of Dirichlet and Neumann divisors. The principal aim of this paper is a detailed theta function representation of all algebro-geometric quasi-periodic solutions and related quantities of the Bsq hierarchy.Comment: LaTeX, 48 page

Quantum Effective Action in Spacetimes with Branes and Boundaries

We construct quantum effective action in spacetime with branes/boundaries. This construction is based on the reduction of the underlying Neumann type boundary value problem for the propagator of the theory to that of the much more manageable Dirichlet problem. In its turn, this reduction follows from the recently suggested Neumann-Dirichlet duality which we extend beyond the tree level approximation. In the one-loop approximation this duality suggests that the functional determinant of the differential operator subject to Neumann boundary conditions in the bulk factorizes into the product of its Dirichlet counterpart and the functional determinant of a special operator on the brane -- the inverse of the brane-to-brane propagator. As a byproduct of this relation we suggest a new method for surface terms of the heat kernel expansion. This method allows one to circumvent well-known difficulties in heat kernel theory on manifolds with boundaries for a wide class of generalized Neumann boundary conditions. In particular, we easily recover several lowest order surface terms in the case of Robin and oblique boundary conditions. We briefly discuss multi-loop applications of the suggested Dirichlet reduction and the prospects of constructing the universal background field method for systems with branes/boundaries, analogous to the Schwinger-DeWitt technique.Comment: LaTeX, 25 pages, final version, to appear in Phys. Rev.

On the efficient Monte Carlo implementation of path integrals

We demonstrate that the Levy-Ciesielski implementation of Lie-Trotter products enjoys several properties that make it extremely suitable for path-integral Monte Carlo simulations: fast computation of paths, fast Monte Carlo sampling, and the ability to use different numbers of time slices for the different degrees of freedom, commensurate with the quantum effects. It is demonstrated that a Monte Carlo simulation for which particles or small groups of variables are updated in a sequential fashion has a statistical efficiency that is always comparable to or better than that of an all-particle or all-variable update sampler. The sequential sampler results in significant computational savings if updating a variable costs only a fraction of the cost for updating all variables simultaneously or if the variables are independent. In the Levy-Ciesielski representation, the path variables are grouped in a small number of layers, with the variables from the same layer being statistically independent. The superior performance of the fast sampling algorithm is shown to be a consequence of these observations. Both mathematical arguments and numerical simulations are employed in order to quantify the computational advantages of the sequential sampler, the Levy-Ciesielski implementation of path integrals, and the fast sampling algorithm.Comment: 14 pages, 3 figures; submitted to Phys. Rev.