On the existence and uniqueness of the solution of the coefficient inverse problem for a semilinear parabolic equation

In this paper, we consider the problem of determining the source function and the coefficient by the derivative with respect to time in a semilinear parabolic equation with overdetermination conditions defined on two different hyperplanes. The existence and uniqueness theorems of the classical solution of the posed coefficient inverse problem in the class of smooth bounded functions were proved. An example of input data satisfying the conditions of the proved theorems is given.

Distant Reading of the Metadata of the Digitized Hungarian Charm Corpus

Based on Éva Pócs’ manual charm index an online database was created for Hungarian verbal charms within the East–West Research Group at the Institute of Ethnology, Hungarian Academy of Sciences (Budapest), between 2013 and 2018. The main goal was to create a multidimensional digital database. Digital text preparation would open the gates to new interpretations and analyses, which would bring us closer to understanding the compound and complex phenomena of charms. In the Digital Database of Hungarian Verbal Charms users can search by various metadata, like date and place of collection/recording, name of collector/scribe, informant, type of source, function of the charm, rites/gestures, language of the text, keywords etc. This paper focuses on how different new arrangements and distant reading of the corpora can reshape our knowledge about the Hungarian verbal charms.

Constraining the annihilation of dark matter via cosmic-ray positrons and electrons

We aim to constrain the properties of dark matter particles by several measurements of positrons and electrons from cosmic-rays. We assume that collisions of dark matter particles and dark matter anti-particles can produce positrons and electrons. The electron-positron propagation is explained by a diffusion-loss equation including loss rates, diffusion, as well as source function. We use data of cosmic-ray positrons and electrons detected by PAMELA, H.E.S.S., AMS-02 and Fermi-LAT. We compare the observational data with the electron and positron spectrum from five annihilation channels in our model to derive constraining factors regarding the cross-section of the annihilation of dark matter. The tightest constraint is provided by cosmic-ray positrons of AMS-02 for the electron channel. Dark matter with mass below a few GeV gets excluded by the cosmic-ray positrons of AMS-02 for the electron, muon and tau channels.

Interpreting the different emissive properties of cyclic triimidazole-based CuI and AgI coordination polymers: a QTAIM and IQA study

A QTAIM and IQA investigation on model compounds of two isostructural AgI and CuI coordination polymers (CPs) based on cyclic triimidazole (L), i.e. the [MIL] n 1D double-stranded stair chain and the [MClL] n 3D network (M = Cu, Ag), has allowed light to be shed on the different emissive behaviour associated with the two metal ions. According to a previously reported investigation [Malpicci et al. (2021). Inorg. Chem. Front. 8, 1312–1323], AgI CPs showed both fluorescence and multiple ligand-centred room-temperature phosphorescences, whereas CuI CPs displayed non-thermally equilibrated halogen and metal-to-ligand charge transfer and two ligand-centred phosphorescences, the latter observed only by their selective activation. Analysis of both local and integral QTAIM descriptors, including delocalization indices and source function, of the Ag—N and Cu—N bonds reveals a higher covalent and local character for the latter, explaining the greater metal–ligand electronic communication observed for the Cu compounds. Moreover, IQA investigation shows that the Cu—N bond is characterized by higher interaction energy, due to both higher electrostatic and exchange-correlation contributions. Analysis on the M—X (M = Ag, Cu; X = I, Cl) bonds, also present in these structures, highlights a much higher covalent and local character with respect to the M—N bonds.

It’s all Greek to me: Explaining, computing, and summarizing traditional and (re)emerging metrics of reliability for seven measures in sexual science

Sexual scientists typically default to appraising the reliability of their self-report measures by calculating one or more α coefficients. Despite the prolific use of α, few researchers understand how to situate and make sense of α within the psychometric theories used to develop the measures used in their research (e.g., latent variable theory) and many unknowingly violate the assumptions of α. In this paper, we describe the disconnect between α and latent variable theory and the subsequent restrictive assumptions α makes. Simultaneously, we introduce an alternative metric of reliability—omega (ɷ)—that is compatible with latent variable theory. Subsequently, we provide a tutorial to walk readers through didactic examples on how to calculate ɷ metrics of reliability using the getOmega() function—a simple open-source function we created to automate the estimation of ɷ. We then introduce the Measurement of Sexuality and Intimacy Constructs (MoSaIC) project to provide insight into the state of reliability in sexuality science. We do this through contrasting α and ɷ estimates of reliability across seven sexuality measures, selected based on their emerging and pre-existing relevance and influence in the field of sexuality, in both a queer (LGBTQ+) sample ( n = 545) and a United States’ representative sample ( n = 548). We finish our paper with pragmatic suggestions for editors, reviewers, and authors. By more deeply understanding one’s options of reliability metrics, sexual scientists may carefully consider how they present and assess their measures’ reliability, and ultimately help improve our science’s replicability.

Boundedness of planar jump discontinuities for homogeneous hyperbolic systems

Suppose that [Formula: see text] is a homogeneous constant coefficient strongly hyperbolic partial differential operator on [Formula: see text] and that [Formula: see text] is a characteristic hyperplane. Suppose that in a conic neighborhood of the conormal variety of [Formula: see text], the characteristic variety of [Formula: see text] is the graph of a real analytic function [Formula: see text] with [Formula: see text] identically equal to zero or the maximal possible value [Formula: see text]. Suppose that the source function [Formula: see text] is compactly supported in [Formula: see text] and piecewise smooth with singularities only on [Formula: see text]. Then the solution of [Formula: see text] with [Formula: see text] for [Formula: see text] is uniformly bounded on [Formula: see text]. Typically when [Formula: see text] on the conormal variety, the sup norm of the jump in the gradient of [Formula: see text] across [Formula: see text] grows linearly with [Formula: see text].

Numerical Experimental for an Inverse Source Problem Method

This paper examines extensions of an iterative method for inverse evaluation of the source function for two elliptic systems. The method begins with a starting value for the undetermined source. Next, a background field and equations for the error field are obtained. 2-D domains are considered. This method is suitable for Helmholtz and Poisson operators. In the presence of finite-difference grid resolution, a varying amount of boundary data, and methods of filtering the noise in the boundary data and the noise intensity of the boundary data, the performance, accuracy, and iteration count of the algorithm are investigated. Keywords: Source, Inverse Problems, Poisson, Noise, Ill-Posedness, Well-Posed

String Comparison in XSLT with tan:diff()

Classical models of string comparison have been difficult to implement in XSLT, in part because those models are designed for imperative, stateful programming. In this article I introduce tan:diff(), an XSLT function built upon a different approach to string comparison, one more conducive to a declarative, stateless language. tan:diff() is efficient and fast, even on pairs of very long strings (100K to 1M characters), in part because of its staggered-sample approach, in part because of its stategies for optimizing enormous strings (> 1M characters). Its results are of optimal quality: the function normally returns a minimal diff (shortest edit script). As an open-source function, tan:diff() enables developers to incorporate robust text comparison directly into XML applications.

New Method for Calculating Bottom Hole Pressure of Horizontal Well in Fracture-cavity Reservoir Based on Point Source Function

Accurate determination of unsteady bottom hole pressure helps to monitor and predict well production in real-time. On the premise of fully considering the seepage characteristics of carbonate rock, a new source function suitable for the seepage of carbonate rock is established. It enlarges the application scope of source function theory and lays a theoretical foundation for solving the seepage problem of carbonate rock. This paper presents the process of solving bottom hole pressure step by step. Step 1: Based on the triple media model, the Pedrosa permeability calculation formula is applied to establish the seepage model of the triple media reservoir considering the formation stress sensitivity. Step 2: By perturbation transform and Laplace transform, the point source function considering stress sensitivity in carbonate reservoir is obtained in Laplace space. The point source function in the infinite plate reservoir is obtained by the principle of mirror image and superposition. Step 3: The method of solving the horizontal well pressure under the constant pressure boundary is established. Through literature comparison and numerical simulation, the rationality of the proposed method is verified. Simultaneously, the sensitivity analysis of pressure and pressure derivative is carried out, and the influences of fracture number, fracture angle, fracture half-length, skin factor, horizontal well segment length, and horizontal well segment spacing on pressure and pressure derivative are analyzed in detail. Considering fracture orientation and stress sensitivity, we divide the triple media fracture-vuggy reservoir fluid flow into five stages. The number of fractures and fracture direction mainly affect stage C. In contrast, the length of horizontal subsection and skin factor mainly affect stage B. Stage D is more obvious when the fracture half-length and the horizontal sublevel interval of the horizontal well are small.