Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.

New Algorithms for M-Estimation of Multivariate Scatter and Location

We present new algorithms for M-estimators of multivariate scatter and location and for symmetrized M-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms. The main idea is to utilize a second order Taylor expansion of the target functional and to devise a partial Newton-Raphson procedure. In connection with symmetrized M-estimators we work with incomplete U-statistics to accelerate our procedures initially.

On the CFT operator spectrum at large global charge

We calculate the anomalous dimensions of operators with large global charge J in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral superfield and a W = Φ3 superpotential. Working in a 1/J expansion, we find that the large-J sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge J is always a scalar operator whose dimension ΔJ satisfies the sum rule J2ΔJ−(J22+J4+316)ΔJ−1−(J22+J4+316)ΔJ+1=0.04067 up to corrections that vanish at large J . The spectrum of low-lying excited states is also calculable explcitly: for example, the second-lowest primary operator has spin two and dimension ΔJ+3√. In the supersymmetric case, the dimensions of all half-integer-spin operators lie above the dimensions of the integer-spin operators by a gap of order J+12. The propagation speeds of the Goldstone waves and heavy fermions are 12√ and ±12 times the speed of light, respectively. These values, including the negative one, are necessary for the consistent realization of the superconformal symmetry at large J.

A Proof-Theoretic Analysis of Theories for Stratified Inductive Definitions

In this article we study subsystems SIDᵥ of the theory ID₁ in which fixed point induction is restricted to properly stratified formulas.

Failures and complications in patients with birth defects restored with fixed dental prostheses and single crowns on teeth and/or implants

OBJECTIVES: To assess retrospectively, over at least 5 years, the incidences of technical and biological complications and failures in young adult patients with birth defects affecting the formation of teeth. MATERIAL AND METHODS: All insurance cases with a birth defect that had crowns and fixed dental prostheses (FDPs) inserted more than 5 years ago were contacted and asked to participate in a reexamination. RESULTS: The median age of the patients was 19.3 years (range 16.6-24.7 years) when prosthetic treatment was initiated. Over the median observation period of 15.7 years (range 7.4-24.9 years) and considering the treatment needs at the reexamination, 19 out of 33 patients (58%) with reconstructions on teeth remained free from all failures or complications. From the patients with FDPs and single unit crowns (SCs) on implants followed over a median observation period of 8 years (range 4.6-15.3 years), eight out of 17% or 47% needed a retreatment or repair at some point due to a failure or a complication. From the three groups of patients, the cases with amelogenesis/dentinogenesis imperfecta demonstrated the highest failure and complication rates. In the cases with cleft lip, alveolus and palate (CLAP) or hypodontia/oligodontia, 71% of the SCs and 73% of the FDPs on teeth (FDP T) remained complication free over a median observation period of about 16 years. Sixty-two percent of the SCs and 64% of the FDPs on implants remained complication free over 8 years. Complications occurred earlier with implant-supported reconstructions. CONCLUSIONS: Because healthy, pristine teeth can be left unprepared, implant-supported SCs and FDPs are the treatment choice in young adults with birth defects resulting in tooth agenesis and in whom the edentulous spaces cannot be closed by means of orthodontic therapy. However, the trend for earlier and more frequent complications with implant-supported reconstructions in young adults, expecting many years of function with the reconstructions, has to be weighed against the benefits of keeping teeth unprepared. In cases with CLAP in which anatomical conditions render implant placement difficult and in which teeth adjacent to the cleft require esthetic corrections, the conventional FDP T still remains the treatment of choice.

The von Mises-Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time

A characterization is provided for the von Mises–Fisher random variable, in terms of first exit point from the unit hypersphere of the drifted Wiener process. Laplace transform formulae for the first exit time from the unit hypersphere of the drifted Wiener process are provided. Post representations in terms of Bell polynomials are provided for the densities of the first exit times from the circle and from the sphere.

Fixed and Flexible: Coexistence of Obligate and Facultative Migratory Strategies in a Freshwater Fish

Migration is an important event in many animal life histories, but the degree to which individual animals participate in seasonal migrations often varies within populations. The powerful ecological and evolutionary consequences of such partial migration are now well documented, but the underlying mechanisms are still heavily debated. One potential mechanism of partial migration is between-individual variation in body condition, where animals in poor condition cannot pay the costs of migration and hence adopt a resident strategy. However, underlying intrinsic traits may overrule such environmental influence, dictating individual consistency in migratory patterns. Unfortunately, field tests of individual consistency compared to the importance of individual condition on migratory propensity are rare. Here we analyse 6 years of field data on roach migration, gathered by tagging almost 3000 individual fish and monitoring their seasonal migrations over extended periods of time. Our aims were to provide a field test of the role of condition in wild fish for migratory decisions, and also to assess individual consistency in migratory tendency. Our analyses reveal that (1) migratory strategy, in terms of migration/residency, is highly consistent within individuals over time and (2) there is a positive relationship between condition and the probability of migration, but only in individuals that adopt a migratory strategy at some point during their lives. However, life-long residents do not differ in condition to migrants, hence body condition is only a good predictor of migratory tendency in fish with migratory phenotypes and not a more general determinant of migratory tendency for the population. As resident individuals can achieve very high body condition and still remain resident, we suggest that our data provides some of the first field evidence to show that both facultative and obligate strategies can co-exist within populations of migratory animals.