A General and Intuitive Envelope Theorem

We present an envelope theorem for establishing first-order conditions in decision problems involving continuous and discrete choices. Our theorem accommodates general dynamic programming problems, even with unbounded marginal utilities. And, unlike classical envelope theorems that focus only on differentiating value functions, we accommodate other endogenous functions such as default probabilities and interest rates. Our main technical ingredient is how we establish the differentiability of a function at a point: we sandwich the function between two differentiable functions from above and below. Our theory is widely applicable. In unsecured credit models, neither interest rates nor continuation values are globally differentiable. Nevertheless, we establish an Euler equation involving marginal prices and values. In adjustment cost models, we show that first-order conditions apply universally, even if optimal policies are not (S,s). Finally, we incorporate indivisible choices into a classic dynamic insurance analysis.

Corrigendum to “The envelope theorem for multiobjective convex programming via contingent derivatives” [J. Math. Anal. Appl. 372 (1) (2010) 197–207]

The aim of this note is to formulate an envelope theorem for vector convex programs. This version corrects an earlier work, “The envelope theorem for multiobjective convex programming via contingent derivatives” by Jiménez Guerra et al. (2010) [3]. We first propose a necessary and sufficient condition allowing to restate the main result proved in the alluded paper. Second, we introduce a new Lagrange multiplier in order to obtain an envelope theorem avoiding the aforementioned error.

A natural extension of the classical envelope theorem in vector differential programming

The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming. The obtained result allows us to measure the quantitative behaviour of a certain set of optimal values (not necessarily a singleton) characterized to become minimum when the objective function is composed with a positive function, according to changes of any of the parameters which appear in the constraints. We show that the sensitivity of the program depends on a Lagrange multiplier and its sensitivity.

Asymmetry of the Aharonov-Bohm diffraction pattern and Ehrenfests theorem

The electron-diffraction pattern for two slits with magnetic flux confined to an inaccessible region between them is calculated. The Aharonov-Bohm effect gives a diffraction pattern that is asymmetric but has a symmetric envelope. In general, both the expected displacement and the kinetic momentum of the electron are nonzero as a consequence of the asymmetry. Nevertheless, Ehrenfests theorems and the conservation of momentum are satisfied. © 1992 The American Physical Society.

A Goldstone theorem in thermal relativistic quantum field theory

We prove a Goldstone theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of spacelike decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3526961]

An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

A NEW PROOF OF OKAJI'S THEOREM FOR A CLASS OF SUM OF SQUARES OPERATORS

Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form ""sum of squares"", satisfying Hormander's bracket condition. Let q be a characteristic point; for P. We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji Show that P is analytic hypoelliptic at q. Hence Okaji has established the validity of Treves' conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of this fact.

Falling sheet envelope method for non-destructive testing time-dependent signals

In this work, an algorithm to compute the envelope of non-destructive testing (NDT) signals is proposed. This method allows increasing the speed and reducing the memory in extensive data processing. Also, this procedure presents advantage of preserving the data information for physical modeling applications of time-dependent measurements. The algorithm is conceived to be applied for analyze data from non-destructive testing. The comparison between different envelope methods and the proposed method, applied to Magnetic Bark Signal (MBN), is studied. (C) 2010 Elsevier Ltd. All rights reserved.

Isolation and characterization of a Clostridium sp with cinnamoyl esterase activity and unusual cell envelope ultrastructure

Microorganisms that hydrolyse the ester linkages between phenolic acids and polysaccharides in plant cell walls are potential sources of enzymes for the degradation of lignocellulosic waste. An anaerobic, mesophilic, spore-forming, xylanolytic bacterium with high hydroxy cinnamic acid esterase activity was isolated from the gut of the grass-eating termite Tumilitermes pastinator. The bacterium was motile and rod-shaped, stained gram-positive, had an eight-layered cell envelope, and.formed endospores. Phylogenetic analysis based on 16S rRNA indicated that the bacterium is closely related to Clostridium xylanolyticum and is grouped with polysaccharolytic strains of clostridia. A wide range of carbohydrates were fermented, and growth was stimulated by either xylan or cellobiose as substrates. The bacterium hydrolysed and then hydrogenated the hydroxy cinnamic acids (ferulic and p-coumaric acids), which are esterified to arabinoxylan in plant cell walls. Three cytoplasmic enzymes with hydroxy cinnamic acid esterase activity were identified using non-denaturing gel electrophoresis. This bacterium possesses an unusual multilayered cell envelope in which both leaflets of the cytoplasmic membrane, the peptidoglycan layer and the S layer are clearly discernible. The fate of all these components was easily followed throughout the endospore formation process. The peptidoglycan component persisted during the entire morphogenesis. It was seen to enter the septum and to pass with the engulfing membranes to surround the prespore. It eventually expanded to form the cortex, verification for the peptidoglycan origin of the cortex. Sporogenic vesicles, which are derived from the cell wall peptidoglycan, were associated with the engulfment process. Spore coat fragments appeared early, in stage II, though spore coat formation was not complete until after cortex formation.

On the Jager-Kaul theorem concerning harmonic maps

In 1983, Jager and Kaul proved that the equator map u*(x) = (x/\x\,0) : B-n --> S-n is unstable for 3 less than or equal to n less than or equal to 6 and a minimizer for the energy functional E(u, B-n) = integral B-n \del u\(2) dx in the class H-1,H-2(B-n, S-n) with u = u* on partial derivative B-n when n greater than or equal to 7. In this paper, we give a new and elementary proof of this Jager-Kaul result. We also generalize the Jager-Kaul result to the case of p-harmonic maps.

On the theory of mixing-frequency electron spin-echo envelope modulation spectroscopy

It has recently been stated that the parametrization of the time variables in the one-dimensional (I-D) mixing-frequency electron spin-echo envelope modulation (MIF-ESEEM) experiment is incorrect and hence the wrong frequencies for correlated nuclear transitions are predicted. This paper is a direct response to such a claim, its purpose being to show that the parametrization in land 2-D MIF-ESEEM experiments possesses the same form as that used in other 4-pulse incrementation schemes and predicts the same correlation frequencies. We show that the parametrization represents a shearing transformation of the 2-D time-domain and relate the resulting frequency domain spectrum to the HYSCORE spectrum in terms of a skew-projection. It is emphasized that the parametrization of the time-domain variables may be chosen arbitrarily and affects neither the computation of the correct nuclear frequencies nor the resulting resolution. The usefulness or otherwise of the MIF parameters \gamma\ > 1 is addressed, together with the validity of the original claims of the authors with respect to resolution enhancement in cases of purely homogeneous and inhomogeneous broadening. Numerical simulations are provided to illustrate the main points.

Exponential Rates of Convergence in the Ergodic Theorem: A Constructive Approach

We prove that, once an algorithm of perfect simulation for a stationary and ergodic random field F taking values in S(Zd), S a bounded subset of R(n), is provided, the speed of convergence in the mean ergodic theorem occurs exponentially fast for F. Applications from (non-equilibrium) statistical mechanics and interacting particle systems are presented.

Neither Molecular Diversity of the Envelope, Immunosuppression Status, Nor Proviral Load Causes Indeterminate HTLV Western Blot Profiles in Samples From Human T-Cell Lymphotropic Virus Type 2 (HTLV-2)-Infected Individuals

Although human T-cell lymphotropic virus type 2 (HTLV-2) is considered of low pathogenicity, serological diagnosis is important for counseling and monitoring. The confirmatory tests most used are Western blot (WB) and PCR. However, in high-risk populations, about 50% of the indeterminate WB were HTLV-2 positives by PCR. The insensitivity of the WB might be due to the use of recombinant proteins of strains that do not circulate in our country. Another possibility may be a high level of immunosuppression, which could lead to low production of virus, resulting in low stimulation of antibody. We found one mutation, proline to serine in the envelope region in the position 184, presented at least 1/3 of the samples, independent the indeterminate WB profile. In conclusion, we found no correlation of immune state, HTLV-2 proviral load, or env diversity in the K55 region and WB indeterminate results. We believe that the only WB kit available in the market is probably more accurate to detect HTLV-1 antibodies, and some improvement for HTLV-2 detection should be done in the future, especially among high-risk population. J. Med. Virol. 82:837-842,2010. (C) 2010 Wiley-Liss, Inc.

A fuzzy max-flow min-cut theorem

Interval-valued versions of the max-flow min-cut theorem and Karp-Edmonds algorithm are developed and provide robustness estimates for flows in networks in an imprecise or uncertain environment. These results are extended to networks with fuzzy capacities and flows. (C) 2001 Elsevier Science B.V. All rights reserved.