Twist-minimal trace formula for holomorphic cusp forms

We derive an explicit formula for the trace of an arbitrary Hecke operator on spaces of twist-minimal holomorphic cusp forms with arbitrary level and character, and weight at least 2. We show that this formula provides an efficient way of computing Fourier coefficients of basis elements for newform or cusp form spaces. This work was motivated by the development of a twist-minimal trace formula in the non-holomorphic case by Booker, Lee and Strömbergsson, as well as the presentation of a fully generalised trace formula for the holomorphic case by Cohen and Strömberg.

ADAPTIVE RESOURCES OF SUBJECTS WITH DIFFERENT STRATEGIES FOR CHOOSING A WAY OF LIFE IN A STRESS SITUATION OF ORGANIZATIONAL CHANGES

Background. The modern world is characterized by instability, uncertainty, complexity and ambiguity. Therefore, a successful development of an organization requires organizational changes, which provoke the necessity of adaptation for people working in this organization. The study of specific adaptive resources revealed the benefits of a differentiated approach to personnel undergoing organizational changes. The differentiation of the sample depending on the strategies for choosing a way of life is justified. Aim. The paper aims to study the specifics of adaptive resources in the context of organizational changes and the features of experiencing stress, tolerance to uncertainty and resilience. Materials and methods. The study involved 208 employees of a large industrial enterprise in Chelyabinsk (of which 135 females and 73 males). The following methods were used during the study: typology for a personal choice of a way of life by V. Gryazeva-Dobshinskaya, A.S. Maltseva; the Psychological Stress Measure (PSM) by L. Lemyrr, R. Tessier, L. Fillion (adapted by N.E. Vodopyanova); the Hardiness test by S. Maddi (adapted by D. A. Leontiev, E. V. Rasskazova); the tolerance to uncertainty scale adapted by E.G. Lukovitskaya. For statistical processing, discriminant and factor analysis were used. Results. General (nonspecific) adaptive resources were revealed: in all subjects regardless of their strategies for choosing a way of life, an inverse correlation was found between stress exposure and resilience as stress resistance resources. Specific adaptive resources were identified: subjects of a hedonistic type had a positive attitude towards new, diverse situations in life and were characterized by a preference for uncertainty; subjects of a value-oriented type were characterized by an arbitrary level of attitude to uncertain and complex situations; creative subjects demonstrated a set of properties, including “challenge” and all the components of “uncertainty tolerance”.

An Error Analysis Toolkit for Binned Counting Experiments

We introduce the MINERvA Analysis Toolkit (MAT), a utility for centralizing the handling of systematic uncertainties in HEP analyses. The fundamental utilities of the toolkit are the MnvHnD, a powerful histogram container class, and the systematic Universe classes, which provide a modular implementation of the many universe error analysis approach. These products can be used stand-alone or as part of a complete error analysis prescription. They support the propagation of systematic uncertainty through all stages of analysis, and provide flexibility for an arbitrary level of user customization. This extensible solution to error analysis enables the standardization of systematic uncertainty definitions across an experiment and a transparent user interface to lower the barrier to entry for new analyzers.

Revealing a full quantum ladder by nonlinear spectroscopy

Coherent two-dimensional spectroscopy in the IR or the visible region is very effective for studying correlations, energy relaxation/transfer pathways in complex multi-chromophore or multi-mode systems. However, it is usually restricted up to two-quanta excitations and their properties. In this paper, an arbitrary level of excitation is suggested as the utility to scan nonlinear potential surfaces of quantum systems up to a desired excitation degree. This can be achieved by a simple three-pulse laser spectroscopy approach. Accurate evaluation of high-level anharmonicities as well as transition amplitudes can be directly obtained. Additionally, questions regarding the quantum nature of the probed system can be addressed by studying absolute peak positions.

A BESSEL DELTA METHOD AND EXPONENTIAL SUMS FOR GL(2)

In this paper, we introduce a simple Bessel $\delta $-method to the theory of exponential sums for $\textrm{GL}_2$. Some results of Jutila on exponential sums are generalized in a less technical manner to holomorphic newforms of arbitrary level and nebentypus. In particular, this gives a short proof for the Weyl-type subconvex bound in the $t$-aspect for the associated $L$-functions.