On a class of gauged nonlinear Schrödinger equations with harmonic potential and supercritical exponential growth

This paper is concerned with the Cauchy problem for a nonlinear Schrödinger equation with a harmonic potential and exponential growth nonlinearity in two space dimensions. In the defocusing case, global well-posedness is obtained. In the focusing case, existence of nonglobal solutions is discussed via potential-well arguments.

1-d Quantum harmonic oscillator with time quasi-periodic quadratic perturbation: Reducibility and growth of Sobolev norms

We study normal diffusive and subdiffusive processes in a harmonic potential (Ornstein-Uhlenbeck process) on a uniformly growing or contracting domain. Our starting point is a recently derived fractional Fokker-Planck equation, which covers both the case of Brownian diffusion and the case of a subdiffusive continuous-time random walk (CTRW). We find a high sensitivity of the random walk properties to the details of the domain growth rate, which gives rise to a variety of regimes with extremely different behaviors. At the origin of this rich phenomenology is the fact that the walkers still move while they wait to jump, since they are dragged by the deterministic drift arising from the domain growth. Thus, the increasingly long waiting times associated with the aging of the subdiffusive CTRW imply that, in the time interval between two consecutive jumps, the walkers might travel over much longer distances than in the normal diffusive case. This gives rise to seemingly counterintuitive effects. For example, on a static domain, both Brownian diffusion and subdiffusive CTRWs yield a stationary particle distribution with finite width when a harmonic potential is at play, thus indicating a confinement of the diffusing particle. However, for a sufficiently fast growing or contracting domain, this qualitative behavior breaks down, and differences between the Brownian case and the subdiffusive case are found. In the case of Brownian particles, a sufficiently fast exponential domain growth is needed to break the confinement induced by the harmonic force; in contrast, for subdiffusive particles such a breakdown may already take place for a sufficiently fast power-law domain growth. Our analytic and numerical results for both types of diffusion are fully confirmed by random walk simulations.

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L1 norm or even sub-linear potentials corresponding to quasinorms Lp (0<p<1). The back side of these approaches is increase in computational cost for optimization. Till so far, no approaches have been suggested to deal with arbitrary error functionals, in a flexible and computationally efficient framework. In this paper, we develop a theory and basic universal data approximation algorithms (k-means, principal components, principal manifolds and graphs, regularized and sparse regression), based on piece-wise quadratic error potentials of subquadratic growth (PQSQ potentials). We develop a new and universal framework to minimize arbitrary sub-quadratic error potentials using an algorithm with guaranteed fast convergence to the local or global error minimum. The theory of PQSQ potentials is based on the notion of the cone of minorant functions, and represents a natural approximation formalism based on the application of min-plus algebra. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off. We demonstrate that on synthetic and real-life datasets PQSQ-based machine learning methods achieve orders of magnitude faster computational performance than the corresponding state-of-the-art methods, having similar or better approximation accuracy.

A few years ago Avetissian {\\it et al.} \\cite{Avetissian2014,Avetissian2015}\ndiscovered that the exponential growth rate of the stimulated annihilation\nphotons from a singlet positronium Bose-Einstein condensate should be\nproportional to the square root of the positronium number density, not to the\nnumber density itself. In order to elucidate this surprising result obtained\nvia a field-theoretical analysis, we point out that the basic physics involved\nis the same as that of resonant subharmonic transitions between two quantum\noscillators. Using this model, we show that nonlinearities of the type\ndiscovered by Avetissian {\\it et al.} are not unique to positronium and in fact\nwill be encountered in a wide range of systems that can be modeled as\nnonlinearly coupled quantum oscillators.\n

We study cuscuton inflation for the models where the potential of the cuscuton takes quadratic and exponential forms. We find that for the quadratic potential, a scalar spectral index n_s is not affected by cuscuton at the leading order in the slow-roll inflation models. However, a tensor-to-scalar ratio r can be suppressed. For the exponential potential of cuscuton, we find the condition for which the inflation has a graceful exit. Under this condition, the observational predictions in this model differ by a few percent from those found in standard inflation. We also examine the particle production due to parametric resonances in both models. We find that in Minkowski space the stage of parametric resonances can be described by the Mathieu equation. For the case where the cuscuton has quadratic potential, the amplitude of the driving force in the Mathieu equation has a similar form as that in standard inflation. Nevertheless, in the case of exponential potential, the amplitude of the driving force decreases faster than that in the standard case. However, parametric resonances in our models can be sufficiently broad possible for the exponential growth of the number of particles. We briefly discuss the case in which the expansion of space is taken into account.

We study resolvents and spectral projections for quadratic differential operators under an assumption of partial ellipticity. We establish exponential-type resolvent bounds for these operators, including Kramers–Fokker–Planck operators with quadratic potentials. For the norms of spectral projections for these operators, we obtain complete asymptotic expansions in dimension one, and for arbitrary dimension, we obtain exponential upper bounds and the rate of exponential growth in a generic situation. We furthermore obtain a complete characterization of those operators with orthogonal spectral projections onto the ground state.

With the increasing availability and use of modern brain diagnostic imaging modalities, discovery of incidental meningiomas has become fairly common. This creates a dilemma among neurosurgeons as to whether these lesions should be treated. Numerous natural history studies have been published in an effort to shed light on the potential for growth of incidental meningiomas. The available data appear to suggest that these tumors can fall into 1 of 3 main growth patterns: no growth, linear growth, or exponential growth. The therapeutic strategy selected should also consider several other factors, mainly the risk of complications from an eventual surgery, the possibility of malignancies and other pathological conditions that mimic meningiomas, and the age and medical condition of the patient. The authors believe that most asymptomatic incidental meningiomas can be observed using serial imaging and clinical follow-up evaluations. Surgical interventions are typically reserved for large, symptomatic lesions and those with documented potential for significant growth.

Axions and axion-like particles (ALPs) are among the most popular candidates that explain the origin of the mysterious dark matter. The most popular ALP production mechanism studied in the literature is the misalignment mechanism, where an ALP field with a quadratic or cosine potential has negligible kinetic energy initially, and it starts oscillating when its mass becomes comparable to the Hubble scale. Recently, there has been an interest in models that go beyond the standard assumptions. These models not only extend the ALP dark matter parameter space, but also provide a rich phenomenology which is absent in the standard scenario. In particular, the ALP fluctuations grow exponentially via parametric resonance and tachyonic instabilities. In this proceeding, we will first demonstrate why the standard paradigm cannot explain dark matter in experimentally interesting parts of the parameter space, and then we will give an overview of the alternative production mechanism with which this issue can be resolved. We will then discuss the exponential growth of the fluctuations in these models. Finally, we will comment on the observational consequences of the exponential growth and show that a sizable region of the ALP parameter space becomes testable even if ALPs have only gravitational interactions.

We consider the linear Wigner–Fokker–Planck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator potential. For a certain class of perturbations we prove that the equation admits a unique stationary solution in a weighted Sobolev space. A key ingredient of the proof is a new result on the existence of spectral gaps for Fokker–Planck type operators in certain weighted L2-spaces. In addition we show that the steady state corresponds to a positive density matrix operator with unit trace and that the solutions of the time-dependent problem converge towards the steady state with an exponential rate.

Growth in minimal salts medium meant that a microorganism has the full repertoire of biosynthetic machinery for surviving in habitats lacking in vitamins and growth factors. This significantly expands the types of habitats suitable for colonization by the microbe. Such evolutionary selected and endowed survival advantage provided a critical growth advantage and colonization potential to particular microbes. Pseudomonas protegens Pf-5 (ATCC BAA-477) potential for growth in minimal salts medium was evaluated by aerobic growth experiments at 25 and 30 oC in M9 medium. Experiment results revealed that the bacterium could grow in M9 medium without nutrient and yeast extract supplementation, but with a long lag phase of 18 hours and a small optical density of 0.7 and 1.0 at 25 and 30 oC, respectively after 45 hours of incubation. Variation in pH, on the other hand, revealed similar pH profiles of net secretion of acidic metabolites during growth in M9 medium, that stabilized prior to attainment of maximal optical density in the cultures at the two temperatures. Supplementation of M9 medium with 1 g/L yeast extract at 25 oC resulted in a shorter lag phase of 3 hours in P. protegens Pf-5 and a maximal optical density of 3.1, which indicated the importance of vitamins and growth factors in yeast extract in supplying necessary building blocks for biomass formation. Similarly, net secretion of acidic metabolites was observed in pH profile prior to exponential phase growth in P. protegens Pf-5, which was followed by a gradual rise in culture broth’s pH. Collectively, P. protegens Pf-5 could grow in minimal salts medium without supplementation of vitamins and growth factors at 25 and 30 oC; thereby, pointing to a significant competitive advantage in survival and colonization of new habitats in the face of nutritional and environmental stressors.

Interactive Effects of Temperature, pH, and Water Activity on the Growth Kinetics of Shiga Toxin–Producing Escherichia coli O104:H4

Regulation of growth in Chinese hamster cells by a local inhibitor

Desiccation resistance and contamination as mechanisms of gaia

Purpose The purpose of this study is to analyze the research trends of halal food small and medium-sized enterprises (SMEs) and provide an overview of future research directions. The halal food industry has seen exponential growth over the past few decades, driven by increasing demand from Muslim consumers worldwide. SMEs play a crucial role in the halal food sector. With the halal food industry, the largest halal industry sector and SMEs the dominant business actor, future research directions that are particularly relevant to halal food SMEs will have major impact for the halal industry as a whole. Design/methodology/approach This investigation used bibliometric analysis, using data from the Scopus database spanning the decade 2013–2022. This study incorporated data visualization and network analysis techniques, implemented through various software tools, including VOSviewer, Scimago Graphica, Bibliometrix and Microsoft Excel. Findings Research on halal SMEs from 2013 to 2022 has consistently increased. Malaysia has conducted the majority of research on halal SMEs. The Journal of Islamic Marketing produced the highest number of research documents in this field. Universiti Utara Malaysia has emerged as the leading institution for research on halal SMEs. Ali MH is the author with the most significant contribution to this area of study. Future research directions in halal SMEs may include topics related to sustainability, social aspects, innovative technology, productivity enhancement and competitiveness. The Ministry of Higher Education Malaysia is the primary funding institution for research and publications on halal food SMEs. Originality/value This study serves as a comprehensive reference and analytical overview of current and prospective research trends in the domain of halal food SMEs. This study aims to provide substantive guidance to scholars, practitioners and government officials regarding the requisite steps to advance research and development in the halal sector. By elucidating the key areas of focus and potential growth, this study seeks to foster a more profound understanding and encourage collaborative efforts to enhance the halal food industry.