We investigate \texorpdfstring{$L_2$}{}-approximation problems in the worst case setting in the weighted Hilbert spaces \texorpdfstring{$H(K_{R_{d,\a,\g}})$}{} with weights \texorpdfstring{$R_{d,\a,{\bm \ga}}$}{} under parameters \texorpdfstring{$1\ge \ga_1\ge \ga_2\ge \cdots\ge 0$ and $1<\az_1\le \az_2\le \cdots$}{}. Several interesting weighted Hilbert spaces \texorpdfstring{$H(K_{R_{d,\a,\g}})$}{} appear in this paper. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. Multivariate approximation; information complexity; tractability; weighted Hilbert spacesWe discuss tractability of \texorpdfstring{$L_2$}{}-approximation problems for the involved Hilbert spaces, which describes how the information complexity depends on \texorpdfstring{$d$}{} and \texorpdfstring{$\va^{-1}$}{}. As a consequence we study the strongly polynomial tractability (SPT), polynomial tractability (PT), weak tractability (WT), and \texorpdfstring{$(t_1,t_2)$}{}-weak tractability (\texorpdfstring{$(t_1,t_2)$}{}-WT) for all \texorpdfstring{$t_1>1$}{} and \texorpdfstring{$t_2>0$}{} in terms of the introduced weights under the absolute error criterion or the normalized error criterion.

We study L_2-approximation problems in the weighted Hilbert spaces in the worst case setting. Three interesting weighted Hilbert spaces appear in this paper, whose weights are equipped with two positive parameters $\ga_j$ and $\az_j$ for $j=1,\,2,\dots,\,d$. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. We discuss the exponential convergence-(t,s)-weak tractability (EC-(t,s)-WT) of these L_2-approximation problems under the absolute or normalized error criterion. In particular, we obtain the sufficient and necessary conditions for EC-(1,1)-WT and EC-(t,1)-WT with t

The aim of this paper is to determine a suitable definition for the concept of fuzzy Hilbert space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Then we considered another approach to the notion of fuzzy inner product and analysed its properties.

Let $(Omega, mu)$ be a measure space and $\{\tau_\alpha\}_{\alpha\in \Omega}$ be a normalized continuous Bessel family for a real Hilbert space $\mathcal{H}$. If the diagonal $\Delta \{(\alpha, \alpha):\alpha \in \Omega\}$ is measurable in the measure space $\Omega\times \Omega$, then we show that \begin{align}\label{CRBA} \sup _{\alpha, \beta \in \Omega, \alpha\neq \beta}\langle \tau_\alpha, \tau_\beta\rangle \geq \frac{-(\mu\times\mu)(\Delta)}{(\mu\times\mu)((\Omega\times\Omega)\setminus\Delta)}. \end{align} We call Inequality (1) as continuous Rankin bound. It improves 76 years old result of Rankin [Ann. of Math., 1947]. It also answers one of the questions asked by K. M. Krishna in the paper [Continuous Welch bounds with applications, Commun. Korean Math. Soc., 2023]. We also derive Banach space version of Inequality (1).

In this paper, we study the weighted reproducing kernels. We introduce a generalization of weighted reproducing property and extend it to relative reproducing property on Banach spaces. This generalization will develop the parallel computing and it can be used as a base of parallel learning for machines especially in the case that there are non-homogenous weighted hypothesis. This methods formulate learning and estimation problems in a relative reproducing kernel Banach space (RRKBS) of functions defined on the data domain, expanded in terms of a kernel.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2},\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2}% ,\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

We consider a stationary inclusion in a real Hilbert space X, governed by a set of constraints K, a nonlinear operator A and an element f∈X. Under appropriate assumptions on the data the inclusion has a unique solution, denoted by u. We state and prove a covergence criterion, i.e., we provide necessary and sufficient conditions on a sequence {un}⊂X which guarantee its convergence to the solution u. We then present several applications which provide the continuous dependence of the solution with respect to the data K, A and f, on one hand, and the convergence of an associate penalty problem, on the other hand. We use these abstract results in the study of a frictional contact problem with elastic materials which, in a weak formulation, leads to a stationary inclusion for the deformation field. Finally, we apply the abstract penalty method in the anlysis of two nonlinear elastic constitutive laws.

Assume that $f:C\rightarrow \mathbb{R}$ is subadditive (superadditive) and hemi-Lebesgue integrable on $C,$ a cone in the linear space $X$ with $0\in C. $ Then for all $x,$ $y\in C$ and a symmetric Lebesgue integrable and nonnegative function $p:\left[ 0,1\right] \rightarrow \lbrack 0,\infty ),$ \begin{align*} \frac{1}{2}f\left( x+y\right) \int_{0}^{1}p\left( t\right) dt& \leq \left( \geq \right) \int_{0}^{1}p\left( t\right) f\left( \left( 1-t\right) x+ty\right) dt \\ & \leq \left( \geq \right) \int_{0}^{1}p\left( t\right) f\left( tx\right) dt+\int_{0}^{1}p\left( t\right) f\left( ty\right) dt. \end{align*} In particular, for $p\equiv 1,$ we have \begin{equation*} \frac{1}{2}f\left( x+y\right) \leq \left( \geq \right) \int_{0}^{1}f\left( \left( 1-t\right) x+ty\right) dt\leq \left( \geq \right) \int_{0}^{1}f\left( tx\right) dt+\int_{0}^{1}f\left( ty\right) dt. \end{equation*} Some particular inequalities related to Jensen's dicrete inequality for convex functions are also given.

A major task in Functional Time Series Analysis is measuring the dependence within and between processes, for which lagged covariance and cross-covariance operators have proven to be a practical tool in well-established spaces. This article deduces estimators and asymptotic upper bounds of the estimation errors for lagged covariance and cross-covariance operators of processes in Cartesian products of abstract Hilbert spaces for fixed and increasing lag and Cartesian powers. We allow the processes to be non-centered, and to have values in different spaces when investigating the dependence between processes. Also, we discuss features of estimators for the principle components of our covariance operators.

While the mobile phone is the world’s most popular media device, it is actually not one single medium, but is effectively used as a different medium by different user groups. The article characterizes polymodal differences in mobile apps usage among different user groups, including gender, education, occupation, screen size, and price. We monitored the complete app usage of 10,725 smartphone users for one month each (56 million sessions, recording almost 1 million hours). Our key contribution consists in developing and analyzing a theoretical framework to classify the over 16,000 apps used into five categories. Exploring nine research questions we provide a broad characterization by asking who, with which characteristics, uses which kinds of apps in what extensity and intensity? For example, it is not the young and high occupational grades that use the mobile phone as a human-to-machine computer (including gaming and artificial intelligence tools). Large screen size is related to extensive long sessions, while a small screen size is related to intensive frequent usage. The results go beyond providing ample empirical evidence for the inherently polymodal nature of the mobile phone, but also proposes a framework on how to possibility deal with it analytically.

In this paper we introduce the hypo-q-norms on a Cartesian product of algebras of bounded linear operators on Hilbert spaces. A representation of these norms in terms of inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar reverses of Cauchy-Buniakowski-Schwarz inequality are also given. Several bounds for the norms δ_p, ϑ_p and the real norms η_r,p and θ_r,p are provided as well.

We address weighted composition operators ψCφ from α-Bloch spaces to Bers-type spaces of bounded holomorphic functions on Y, where Y is a generalized Hua domain of the first kind, and obtain some necessary and sufficient conditions for the boundedness and compactness of those operators.

We introduce the notion of generalized contraction on dualistic partial metric spaces. A fixed point theorem for mappings satisfying above mentioned contraction is obtained. Some consequences of our result are obtained. We construct an example to demonstrate the effectiveness of our result among the corresponding results in partial metric spaces. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. We discuss an application of our fixed point results to show the existence of solution of functional equations.

Splines and quasi-interpolation operators are important both in approximation theory and applications. In this paper, we construct a family of quasi-interpolation operators for the bivariate quintic spline spaces S₅³ (∆_mn⁽²⁾). Moreover, the properties of the proposed quasi-interpolation operators are studied, as well as its applications for solving two-dimensional Burgers’ equation and image reconstruction. Some numerical examples show that these methods, which are easy to implement, provide accurate results.

In this study, we prove the norm separating property for the composition of Cesàro 1 and Gamma matrices with their transpose. As a result, we compute the ℓp-norms of six classes of operators that commute with the infinite Hilbert operators. Additionally, we find the norm of 3 Hilbert’s commutants on some well-known sequence spaces.

This paper is devoted to the study of multi-dimensional integral transform with Fox H-function in the kernel in weighted spaces integrable functions in the domain R+n with positive coordinates. Mapping properties such as the boundedness, the range, the representations of the considered transformation are established.

In this paper, some characterizations of fuzzifying strong compactness are given, including characterizations in terms of nets and pre -subbases. Several characterizations of locally strong compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.

Accurate forecasting of icing thickness has a great significance for ensuring the security and stability of power grid. In order to improve the forecasting accuracy, this paper proposes an icing forecasting system based on fireworks algorithm and weighted least square support vector machine (W-LSSVM). The method of fireworks algorithm is employed to select the proper input features with the purpose of eliminating the redundant influence. In addition, the aim of W-LSSVM model is to train and test the historical data-set with the selected features. The capability of this proposed icing forecasting model and framework is tested through the simulation experiments using real-world icing data from monitoring center of key laboratory of anti-ice disaster, Hunan, South China. The results show that the proposed W-LSSVM-FA method has a higher prediction accuracy and it may be a promising alternative for icing thickness forecasting.

Various means (the arithmetic mean, the geometric mean, the harmonic mean, the power means) are often used as central tendency statistics. A new statistic of such type is offered for a sample from a distribution on the positive semi-axis, the gamma-weighted geometric mean. This statistic is a certain weighted geometric mean with adaptive weights.

Tree ordinances can be an effective means of preserving urban forests in the face of development pressures. Despite this, they also have the potential to be divisive among the public - especially when applied to privately-owned land. In this study we surveyed 1,716 Florida urban residents to understand how they value regulation and management of the urban forest. Specifically, we asked about: tree protection ordinances, incentive programs to manage or plant trees, justification for tree removal, and development. Most respondents supported tree protections, even when applied to trees on their own property or when they had the potential to limit development activities. Additionally, there was limited support for removing healthy trees for development. Respondents supported the use of funds for urban forestry efforts – particularly at the local or state level.

The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its extensive use in optics, engineering, and signal processing. In the present work, we aimed to expand the fractional Hilbert transform to a space of generalized functions known as Boehmians. We introduce a new fractional convolution operator for the fractional Hilbert transform to prove a convolution theorem similar to the classical Hilbert transform and also to extend the fractional Hilbert transform to Boehmians. We also construct a suitable Boehmian space on which the fractional Hilbert transform exists. Further, we investigate convergence of the fractional Hilbert transform for the class of Boehmians and discuss the continuity of the extended fractional Hilbert transform.

Discrete Double Hilbert Exponential sums along polynomials. This is preprint version (not peer reviewed) And we now check the proof of (ii) of Lemma 3.2 whether it is really true.

In a previous paper (https://dx.doi.org/10.2139/ssrn.3648127 ), an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for “n = 3” has been known for a long time. It needs “Hilbert mathematics”, which is inherently complete unlike the usual “Gödel mathematics”, and based on “Hilbert arithmetic” to generalize Peano arithmetic in a way to unify it with the qubit Hilbert space of quantum information. An “epoché to infinity” (similar to Husserl’s “epoché to reality”) is necessary to map Hilbert arithmetic into Peano arithmetic in order to be relevant to Fermat’s age. Furthermore, the two linked semigroups originating from addition and multiplication and from the Peano axioms in the final analysis can be postulated algebraically as independent of each other in a “Hamilton” modification of arithmetic supposedly equivalent to Peano arithmetic. The inductive proof of FLT can be deduced absolutely precisely in that Hamilton arithmetic and the pransfered as a corollary in the standard Peano arithmetic furthermore in a way accessible in Fermat’s epoch and thus, to himself in principle. A future, second part of the paper is outlined, getting directed to an eventual proof of the case “n=3” based on the qubit Hilbert space and the Kochen-Specker theorem inferable from it.

A close analysis of the text of Gen. 2:8-15, pertaining to the garden of Eden, shows the structural differences between said text and others from ancient mythologies that mention or describe a paradise. Likewise, that analysis suggests that the data provided by the Bible to locate paradise is merely a narrative device meant to dissipate all doubts as to the existence of the garden where God put human beings. Similarly to other spaces that appear in the Bible, the garden of Eden is but an impossible place. Throughout the centuries, however, recurring proposals have been made that aim to find paradise. As time went by, those proposals were progressively modified by the intellectual ideas dominant at any given era, thus leading the representations of the location of Paradise further and further away from the information provided by the biblical text.

The paper is a continuation of another paper (https://philpapers.org/rec/PENFLT-2) published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The relevant mathematical structure is Hilbert arithmetic in a wide sense (https://dx.doi.org/10.2139/ssrn.3656179), in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem.

Inspired by works of W. H. Zurek and others, a mathematical, physical theory, entirely within a quantum mechanical formalism, is proposed for cognitive processes in terms of an abstract Hilbert-space for the conscious state that is an exact replica of the Hilbert-space for the neuronic physical state. Thus, any actual state of consciousness arises by its formal alignment (identification) with some-one in the set of the neuronic states, with the latter undergoing perpetual changes in the wake of life-long experiences. It is posited that these changes become expressed by an increase in the number of ordered, coherent neuronic states at the expense of the pre-ordinal random neuronic states. Changes, transitions between states are induced by a Gorini-Kossakowski-Sudarshan-Lindblad formalism, which is also instrumental in the effect of the conscious state on bodily actions. The paradigmatic findings of R.N. Shepard (1958 - 2011) and of S. Sternberg (1966 - 2016) for long- and short-term recalls are interpreted within the model.

The standard approach to integrable nonlinear evolution equations (NLEE) usually uses the following steps: 1) Lax representation $[L,M]=0$; 2)~construction of fundamental analytic solutions (FAS); 3) reducing the inverse scattering problem (ISP) to a Riemann-Hilbert problem (RHP) $\xi^+(x,t,\lambda) =\xi^-(x,t,\lambda) G(x,t\lambda)$ on a contour $\Gamma$ with sewing function $G(x,t,\lambda)$; 4) soliton solutions and possible applications.Step 1) involves several assumptions: the choice of the Lie algebra $\mathfrak{g}$ underlying $L$, as well as its dependence on the spectral parameter, typically linear or quadratic in $\lambda$. In the present paper we propose another approach which substantially extends the classes of integrable NLEE.Its first advantage is that one can effectively use any polynomial dependence in both $L$ and $M$. We use the following steps: A) Start with canonically normalized RHP with predefined contour $\Gamma$; B) Specify the $x$ and $t$ dependence of the sewing function defined on $\Gamma$; C) Introduce convenient parametrization for the solutions $ \xi^\pm(x,t,\lambda)$ of the RHP and formulate the Lax pair and the nonlinear evolution equations (NLEE); D) use Zakharov-Shabat dressing method to derive their soliton solutions. This needs correctly taking into account the symmetries of the RHP. E) Define the resolvent of the Lax operator and use it analyze its spectral properties.

Motivated from the theory of Hilbert-Schmidt morphisms between Hilbert C*-modules over commutative C*-algebras by Stern and van Suijlekom [J. Funct. Anal., 2021], we introduce the notion of p-absolutely summing morphisms between Hilbert C*-modules over commutative C*-algebras. We show that an adjointable morphism between Hilbert C*-modules over monotone closed commutative C*-algebra is 2-absolutely summing if and only if it is Hilbert-Schmidt. We formulate version of Pietsch factorization problem for p-absolutely summing morphisms and solve partially.

Here we present Hilfer-Polya, psi-Hilfer Ostrowski and psi-Hilfer-Hilbert- Pachpatte types fractional inequalities. They are univariate inequalities involving left and right Hilfer and -Hilfer fractional derivatives. All estimates are with respect to norms ||.||p, 1 <_ p <_infinite. At the end we provide applications.

In order to deal with imprecision, ambiguity, and uncertainty in data analysis, Pawlak introduced rough set theory in 1982. This paper aims to expand the scope of basic set theory developed by presenting the notions of δP-upper and δP-lower approximations, that are based on the notion of δP-open sets, we additionally examine a few of their fundamental characteristics.

The present study investigated the effect of art on promoting the meaning of the urban space. In this regard, after considering the semantic dimension of the urban space and the mechanism of transferring the meanings of art through the views of experts, a model is presented for examin-ing the art’s cooperation in promoting urban space meaning in Tehran. In this study, a mixed method was used. In the first stage, the categories of space meanings influenced by art were ex-tracted through using the qualitative method of interpretive phenomenology and by examining 61 in-depth interviews in six urban spaces eligible for urban art in Tehran. In the second stage, these categories were surveyed in these spaces through 600 questionnaires after converting to the questionnaire items. Based on the results, "the possibility of the experience and perception", "social participation", and "the relationship with the context" were the main themes of the se-mantic relationship of art and urban space. Further, the lower scores related to the theme of "so-cial participation" in the quantitative investigations indicated that this theme was weaker than the other themes in promoting the meaning of the urban space through the art in the selected urban spaces.

A class $\mathfrak{M}$ $$ of coarse spaces is called a variety if $\mathfrak{M}$ $$ is closed under formation of subspaces, coarse images and products. We classify the varieties of coarse spaces and, in particular, show that if a variety $\mathfrak{M}$ $$ contains an unbounded metric space then $\mathfrak{M}$ is the variety of all coarse spaces.

A class $\mathfrak{M}$ $$ of coarse spaces is called a variety if $\mathfrak{M}$ $$ is closed under formation of subspaces, coarse images and products. We classify the varieties of coarse spaces and, in particular, show that if a variety $\mathfrak{M}$ $$ contains an unbounded metric space then $\mathfrak{M}$ is the variety of all coarse spaces.

We develop the theory of Heyting locally small spaces, including Stone-like dualities such as a new version of Esakia duality and a system of concrete isomorphisms and equivalences. In such a way, we continue building tame topology, realising Grothendieck's ideas. We use up-spectral spaces and define the standard up-spectralification of a Kolmogorov locally small space. This research gives more understanding of locally definable spaces over structures with topologies.

China is experiencing rapid urbanization. The focus on health issues has shifted from the treatment of diseases to passive or active prevention. Diseases caused by the deterioration of the urban environment, such as cardiovascular disease, diabetes, obesity and other chronic diseases and mental illness, have gradually become the main threat to public health. Studies have confirmed that urban green spaces (UGS) can help residents relieve mental stress, improve mood, reduce mental fatigue and restore attention, which has a positive effect on people's physical and mental health. In this study, the relationship between the quantity and quality factors of UGS and the physical and mental health of urban residents in Xihu District of Hangzhou is examined, and on this basis, UGS design strategies are proposed to promote the physical and mental health of residents. This study is of great significance for the future construction of UGS that are beneficial to the health of residents and the promotion of a healthy China and healthy city construction.

In this paper we survey some recent results due to the author concerning various inequalities and approximations for the finite Hilbert transform of a function belonging to several classes of functions, such as: Lipschitzian, monotonic, convex or with the derivative of bounded variation or absolutely continuous. More accurate estimates in the case that the higher order derivatives are absolutely continuous, are also provided. Some quadrature rules with error bounds are derived. They can be used in the numerical integration of the finite Hilbert transform and, due to the explicit form of the error bounds, enable the user to predict a priory the accuracy.

With the increasingly online exposure of urban public spaces, the new concept of "Internet-celebrity cities" has emerged in China. The online internet-famous sites are the main characteristics of "Internet-celebrity cities". To fully understand online users' preferences in such kind of public spaces, this article took 27 typical riverfront internet-famous sites (RIFS) in Changsha city (China), as an example. Through the online images and review comments on social media platform "Xiaohongshu", the study analyzed users’ perception of RIFS specially on visual and emotional preferences. It revealed the following findings:(1) The popularity of RIFS had a significant head effect and there were far more positive emotions than neutral and negative emotions in review comments. (2) According to 5 different categories of RIFS: modern buildings with river views, restaurants with strong visual impact became the main attractions on commercial RIFS. The art exhibition RIFS attracted visitors to experience traditional culture and highlight their aesthetic pursuits. In the historical and cultural RIFS, people preferred to see the historical buildings with surrounding natural environment, as well as river and mountains views. Ecological Recreational RIFS showed the similar results with the uncultivated RIFS, for the main focus was on the ecological environment, a broader vision and the specific atmosphere. Moreover, the uncultivated RIFS showed more diversified attraction points. This study can provide a new perspective on the waterfront vitality and can offer a targeted and attractive manner for waterfront regeneration that are different from traditional methods.

While many practitioners and experts understand the risks associated with low urban tree diversity, they often lack the ability to rectify issues they encounter on their own. The current system of tree production and procurement is complex – shaped by market pressures, nursery and site constraints, local governance, and differing professional objectives among those who grow, specify, and plant trees. To understand this complexity as well as constraints to- and opportunities for increasing urban tree diversity, we conducted a series of focus groups comprised of nursery growers, landscape architects, and urban foresters. Our results highlight a significant list of considerations and constraints to diversity (both shared among green industries and some specific to growers or purchasers). More importantly, in discussing our findings we outline actionable strategies for increasing urban tree diversity.

In this paper, we introduce the notion of weighted generalized group inverse in a Banach algebra with proper involution. This is a natural generalization of weighted weak group inverse for a complex matrix and Hilbert space operator. We present several characterizations and representations of this generalized inverse. In addition, a new partial order on elements in a Banach *-algebra is investigated by using the weighted generalized group inverse and some known results are thus generalized.

Integrated Kerr micro-combs, a powerful source of many wavelengths for photonic RF and microwave signal processing, are particularly useful for transversal filter systems. They have many advantages including a compact footprint, high versatility, large numbers of wavelengths, and wide bandwidths. We review recent progress on photonic RF and microwave high bandwidth temporal signal processing based on Kerr micro-combs with spacings from 49-200GHz. We cover integral and fractional Hilbert transforms, differentiators as well as integrators. The potential of optical micro-combs for RF photonic applications in functionality and ability to realize integrated solutions is also discussed.

In this article, we establish some new generalized inequalities of Hilbert-type on time scales delta calculus which considered as similar formulas for inequalities of Hilbert type proved by Chang-Jian, Lian-Ying and Cheung [7]. These inequalities will proved by applying Hölder’s inequality, chain rule on time scales and the mean inequality. As special cases of our results (when T = N and T = R), we get the discrete and continuous inequalities. Also, we can obtain other inequalities in different time scale, like T = q^Z, q > 1.

We prove that a diffeological space is diffeomorphic to the categorical join of any generating family of plots.

In the paper we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a closed system of differential equations of Cauchy-type in covariant derivatives. We have found the number of essential parameters which the solution of the system depends on. Similar approach was applied for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-m-symmetric spaces.

In the literature, frames generated by unitary representations of groups (known as group-frames) are studied only for Hilbert spaces. We make first study of frames for Banach spaces generated by isometric invertible representations of discrete groups on Banach spaces. These frames are characterized using left regular, right regular, Gram-matrices and group-matrices on classical sequence spaces. A sufficiently large collection of functional-vector pairs using the double commutant of the representation is identified which generate group-frames for Banach spaces. Subsequently, we study Schauder frames generated by time-frequency shift operators on finite dimensional Banach spaces. We derive Moyal formula, fundamental identity of Gabor analysis, Wexler-Raz criterion and Ron-Shen duality in functional form.

In the present paper we introduce the concept of orthogonal frames in Krein spaces, prove the independence of the choice of the fundamental symmetry, and from this we obtain a number of interesting properties that they satisfy. We show that there is no distinction between orthogonal frames in a Krein space and orthogonal frames in its associated Hilbert. Furthermore, we characterize frames dual to a given frame, which is a useful tool for constructing examples.

In this paper, the concept of fuzzy locally convex spaces generated by a family of fuzzy seminorms is introduced. We prove that a Minkowski functional of zero neighborhoods generates a seminorm and finally deduce that the topology generated by the family of seminorms coincides with that of the Minkowski functional.

The aim of this paper is to discuss the relations between various notions of sequential completeness and the corresponding notions of completeness by nets or by filters in the setting of quasi-metric spaces. We propose a new definition of right $K$-Cauchy net in a quasi-metric space for which the corresponding completeness is equivalent to the sequential completeness. In this way we complete some results of R.~A. Stoltenberg, Proc. London Math. Soc. \textbf{17} (1967), 226--240, and V.~Gregori and J.~Ferrer, Proc. Lond. Math. Soc., III Ser., \textbf{49} (1984), 36. A discussion on nets defined over ordered or pre-ordered directed sets is also included.

Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by quantum neo-Pythagoreanism links it to the opposition of propositional logic, to which Gentzen’s cut rule refers immediately, on the one hand, and the linguistic and mathematical theory of metaphor therefore sharing the same structure borrowed from Hilbert arithmetic in a wide sense. An example by hermeneutical circle modeled as a dual pair of a syllogism (accomplishable also by a Turing machine) and a relevant metaphor (being a formal and logical mistake and thus fundamentally inaccessible to any Turing machine) visualizes human understanding corresponding also to Gentzen’s cut elimination and the Gödel dichotomy about the relation of arithmetic to set theory: either incompleteness or contradiction. The metaphor as the complementing “half” of any understanding of hermeneutical circle is what allows for that Gödel-like incompleteness to be overcome in human thought.

In this paper we establish some weighted integral inequalities of Ostrowski, Čebyšev and Lupaş type. Applications for continuous probability density functions supported on infinite intervals with two examples are also given.

The heterogeneous structure implies that a few nodes may be crucial in maintaining network structural and functional properties. Identifying these crucial nodes correctly and quickly is a primary issue as contemporarily may face the mushrooming of large-scale datasets. Besides, the ‘weight issue’ is always ignored in this field which edge weight may play a positive/negative role in contributing to the node importance in different weighted networks. This paper provides a novel algorithm, Weighted Expectation Algorithm (WEA), which aims to ensure accuracy and speed of computation by taking advantage of dynamic programming to better handle the task of large-scale networks. Additionally, the weight issue that edge weights may contribute differently is addressed by a simply quantitative definition. Two standard experiments show WEA can maintain the network structure in connectivity well (by the lowest average robustness 0.192) and identify the node importance better in the spreading function test of spreading dynamics (by the highest average Kendall’s tau-b 0.678). In addition, the time complexities of different algo-rithms are evaluated, and their time-consuming are tested, proving that WEA consumes a rela-tively short time.

We have estimated the level of Risk Weighted Assets among 30 countries in Europe, in 30 trimesters, using data of the European Banking Authority-EBA of 139 variables. We perform an econometric model using Pooled OLS, Panel Data with Fixed Effects, Panel Data with Random Effects, Weighted Least Squares. We found that Risk Weighted Assets is negatively associated, among others, to the level of NFC loans in mining and quarrying, in public administration and defence, and in financial and insurance activities and positively associated, among others to distribution of NFC loans in human health services and social work activities, in education and the level of net fee and commission income. Furthermore, we apply a cluster analysis with the k-Means algorithm, and we find the presence of two clusters. A comparison was then made between eight different machine learning algorithms for predicting the value of the RWAs and we found that the best predictor is the linear regression. The RWA value is predicted to increase by 1.5%.

Aiming at the defects of low precision and time cumulative error, an external wireless signal weighted centroid localization algorithm aided inertial positioning method is designed in this paper. According to the signal strength of each anchor node received at the test point, the distance between the anchor node and the anchor node is obtained by using the attenuation model of the wireless signal. Three anchor nodes are used to measure the distance between the anchor node and the measured point. We can obtain the area to be measured according to the actual situation, the position of the measured point is obtained by the weighted centroid localization algorithm and a combined model of wireless signal aided inertial navigation system is established. The simulation results show that the method can greatly improve the positioning accuracy and restrain the divergence of the longitude error and latitude error.

To enhance the overall reliability of the power system, engineers have redirected their focus toward health monitoring and early detection of faults in transformers. Among these faults, transformer core defects demand particular attention. While fault simulation using software has traditionally been the preferred approach, these methods suffer from data inaccuracies in real-world conditions. Consequently, conducting actual experimental setups with induced faults is imperative to investigate core issues. This study uses Hilbert Transform (HT) as a signal processing technique to extract crucial data characteristics, thereby enhancing the performance of the classifier model. The research involves analyzing electric current signals from a single-phase 1kVA transformer. A comparative assessment of our proposed model was conducted using raw data and Fast Fourier Transform (FFT), evaluating accuracy, precision, recall, F1-score, and computational time. The results demonstrate a significant improvement in all metrics for the classifier models, particularly the k-nearest neighbor (KNN) algorithm, which exhibited values of 83.89%, 84.39%, 83.89%, 83.79%, and 0.0156 seconds, respectively. Future work aims to extend this analysis under different loading conditions.

This paper is devoted to the study of reproducing kernels on 2-inner product Hilbert spaces. We focus on a new structure to produce reproducing kernel Hilbert and Banach spaces. According to multi-variable computing, this structures can be useful in electrocardiographs, machine learning and economy

In an outstanding article published in 2008, Suzuki obtained a nice generalization of the Banach contraction principle from which derived a characterization of metric completeness. Although Suzuki’s theorem has been successfully generalized and extended in several directions and contexts, we here show by means of a simple example that the problem of achieving, in an obvious way, its full extension to the framework of w-distances does not have an emphatic response. Motivated by this fact we introduce the concept of presymmetric w-distance on metric spaces, we give some properties and examples of this new structure and show that it provides a reasonable setting to obtain a real and hardly forced w-distance generalization of Suzuki’s theorem. This is realized in our main result, which is a fixed point theorem that involves presymmetric w-distances and certain contractions of Suzuki-type. We also discuss the relationship between our main result and the well-known w-distance full generalization of the Banach contraction principle, due to Suzuki and Takahashi. Connected to this approach we prove another fixed point result that compare with our main result through some examples. Finally, we state a characterization of metric completeness by using our fixed point results.

Every subset S of a Cartesian spaces Rd, endowed with differen- tial structure C∞(S) generated by restrictions to S of functions in C∞(Rd), has a canonical partition M(S) by manifolds, which are or- bits of the family X(S) of all derivations of C∞(S) that generate local one-parameter groups of local diffeomorphisms of S. This partition satisfies the frontier condition, Whitney’s conditions A and B. If M(S) is locally finite, then it satisfies all definitions of stratification of S. This result extends to Hausdorff locally Euclidean differential spaces.

We develop the theory of Heyting small spaces and prove a new version of Esakia duality for such spaces. To do this, we notice that spectral spaces may be seen as sober small spaces with all smops compact and introduce the method of the standard spectralification. This helps to understand open continuous definable mappings between definable spaces over o-minimal structures.

The classifier system proposed in this work combines the dissimilarity spaces produced by a set of Siamese neural networks (SNNs) designed using 4 different backbones, with different clustering techniques for training SVMs for automated animal audio classification. The system is evaluated on two animal audio datasets: one for cat and another for bird vocalizations. Different clustering methods reduce the spectrograms in the dataset to a set of centroids that generate (in both a supervised and unsupervised fashion) the dissimilarity space through the Siamese networks. In addition to feeding the SNNs with spectrograms, additional experiments process the spectrograms using the Heterogeneous Auto-Similarities of Characteristics. Once the similarity spaces are computed, a vector space representation of each pattern is generated that is then trained on a Support Vector Machine (SVM) to classify a spectrogram by its dissimilarity vector. Results demonstrate that the proposed approach performs competitively (without ad-hoc optimization of the clustering methods) on both animal vocalization datasets. To further demonstrate the power of the proposed system, the best stand-alone approach is also evaluated on the challenging Dataset for Environmental Sound Classification (ESC50) dataset. The MATLAB code used in this study is available at https://github.com/LorisNanni.

We give a topological condition for a generic sliced space to be globally hyperbolic, without any hypothesis on the lapse function, shift function and spatial metric.

In the radar system, detection represents a basic and important stage in the receiver side. The detection process is based on the thresholding criteria; two philosophies of this criteria, constant and adaptive threshold. The constant threshold is simple in design, but it has a mis-detection and does not control the false alarm rate. As for the adaptive threshold, it is powerful in target detection, and better control of the false alarm rate, where it is called Constant False Alarm Rate (CFAR). Lots of research in the CFAR design, but the gap in the previous works is that there is no CFAR algorithm can be working with all or most environmental fields and all or most target situations.In this paper, The CFAR, which can work with the most environment and most of the target situations, has been presented. The producing the design and implementation of the new practical CFAR processor is presented. Where, the new CFAR is a combination of the properties of three different CFAR algorithm (CA, OSGO, and OSSO), and from two different families; averaging and statistical. Where it has overperformed of it's is 97.25% for simulation and 96.25% for the implementable version for different target situations. The simulation analysis is made by using Matlab 2015, while the implementation is done by using Xilinx Spartan 700 3a.

Containing hundreds of spectral bands (features), hyperspectral images (HSIs) have high ability in discrimination of land cover classes. Traditional HSIs data processing methods consider the same importance for all bands in the original feature space (OFS), while different spectral bands play different roles in identification of samples of different classes. In order to explore the relative importance of each feature, we learn a weighting matrix and obtain the relative weighted feature space (RWFS) as an enriched feature space for HSIs data analysis in this paper. To overcome the difficulty of limited labeled samples which is common case in HSIs data analysis, we extend our method to semisupervised framework. To transfer available knowledge to unlabeled samples, we employ graph based clustering where low rank representation (LRR) is used to define the similarity function for graph. After construction the RWFS, any arbitrary dimension reduction method and classification algorithm can be employed in RWFS. The experimental results on two well-known HSIs data set show that some dimension reduction algorithms have better performance in the new weighted feature space.

In this short communication, following a brief introduction, we undertake a comprehensive analytical study of the weighted Simpson index. Our primary emphasis concerns the precise determination of the optimal point (minimizer) coordinates and of the minimum value of the index, a differentiable convex function, which is related to the harmonic mean concept. Furthermore, we address and solve the inversion problem and show the tight connection between both approaches. Last, we give some insights and final remarks on this subject.

Weighted Student Funding (WSF) systems have been implemented in various countries to give schools more autonomy over how to allocate their funding. School principals use funding to maintain school operations and foster innovation for achieving educational goals. However, despite the importance of this process, scholarly research has largely overlooked how principals make decisions about their financial resources. Accordingly, this study seeks to provide practical insights into the strategies used by one school by highlighting their staff’s perceptions about using their WSF to maintain school operations and spur innovation. Using a case study approach, we investigated a principal who effectively used a school’s WSF to transform a failing school into an innovative one. The findings revealed that the principal strategically implemented financial management mechanisms in a way that inspired teachers to deeply consider how a school's WSF can help achieve educational goals. The principal fostered consensus on the school's direction, encouraged innovation through hands-on experiential learning and strategic planning, and facilitated funding for innovative teachers by guiding proposal development. Insights into the shifting cultural and practical landscape of financial resource utilization within schools are discussed.

In this paper we provide amongst others some simple error bounds in approximating the weighted Riemann-Stieltjes integral $\int_{a}^{b}f\left(t\right) g\left(t\right) dv\left(t\right) $ by the use of three points formula \begin{equation*} f\left(b\right) \int_{c}^{b}g\left(s\right) dv\left(s\right) +f\left(a\right) \int_{a}^{d}g\left( s\right) dv\left( s\right) -f\left(x\right) \int_{c}^{d}g\left(t\right) dv\left(t\right) \end{equation*} where $x,$ $c,$ $d\in \left[a,b\right],$ $g,$ $v:\left[a,b\right] \rightarrow \mathbb{C}$ under bounded variation and Lipschitzian assumptions for the function $f$ and such that the involved Riemann-Stieltjes integrals exist.

This study introduces a new discrete distribution which is a weighted version of Poisson-Lindley distribution. The weighted distribution is obtained using the negative binomial weight function and can be fitted to count data with over-dispersion. The p.m.f., p.g.f. and simulation procedure of the new weighted distribution, namely weighted negative binomial Poisson-Lindley (WNBPL), are provided. The maximum likelihood method for parameter estimation is also presented. The WNBPL distribution is fitted to several insurance datasets, and is compared to the Poisson and negative binomial distributions in terms of several statistical tests.

We demonstrate an RF photonic fractional Hilbert transformer based on an integrated Kerr micro-comb source featuring a record low free spectral range of 49 GHz. By programming and shaping the comb lines according to calculated tap weights for up to 39 wavelengths across the C-band, we achieve tunable bandwidths ranging from 1.2 to 15.3 GHz as well as variable center frequencies from baseband to 9.5 GHz, for both standard integral and arbitrary fractional orders. We experimentally characterize the RF amplitude and phase response of the tunable bandpass and lowpass Hilbert transformers with 90 and 45-degree phase shifts. The experimental results show good agreement with theory, confirming the effectiveness of our approach as a powerful way to implement standard and fractional order Hilbert transformers with broad and variable bandwidths and center frequencies, with high reconfigurability and greatly reduced size and complexity. Tan, and D. J. Moss are with the Optical Sciences Centre, Swinburne University of Technology, Hawthorn, VIC 3122, Australia. (Corresponding e-mail: [email protected]). Xu is with the Electro-Photonics Laboratory, Department of Electrical and Computer System Engineering, Monash University, Clayton, 3800 VIC, Australia

This scoping study aims to explore the relationships between urban green spaces (UGSs) and cancer. We followed the PRISMA extension for scoping reviews (protocol published in 2018). Eligibility criteria for papers were: 1) to be concerned with UGSs, 2) reporting effects of UGSs on cancer-related outcomes including direct or indirect measures, 3) reporting randomized controlled trials, prospective cohort studies, case studies, observational studies, non-comparative studies, 4) in English or French. The search covered primary studies in the published and unpublished (grey) literatures searching by hand and electronic databases (MEDLINE, Green File, CINAHL and ScienceDirect). Among 1703 records screened by two reviewers independently, 29 were included for qualitative synthesis. We classify the cancers concerned and the effects reported i.e. protective effect, risk or without association. The most investigated cancers are bladder, breast and lung cancer. Our study also identified contributing factors and their mediating effects between UGSs and cancer. Results highlight the wide variety of possible mediating factors between the use of green spaces and cancer occurrence, remission and/or prevention. Knowledge gaps and future research perspectives should be oriented to qualitative research on protective factors, the role of mental health in recovering from cancer and health inequalities.

Let $(\{f_n\}_{n=1}^\infty, \{\tau_n\}_{n=1}^\infty)$ and $(\{g_n\}_{n=1}^\infty, \{\omega_n\}_{n=1}^\infty)$ be unbounded continuous p-Schauder frames ($0<p<1$) for a disc Banach space $\mathcal{X}$. Then for every $x \in ( \mathcal{D}(\theta_f) \cap\mathcal{D}(\theta_g))\setminus\{0\}$, we show that \begin{align}\label{UB} \|\theta_f x\|_0\|\theta_g x\|_0 \geq \frac{1}{\left(\displaystyle\sup_{n,m \in \mathbb{N} }|f_n(\omega_m)|\right)^p\left(\displaystyle\sup_{n, m \in \mathbb{N}}|g_m(\tau_n)|\right)^p}, \end{align} where \begin{align*} & \theta_f: \mathcal{D}(\theta_f) \ni x \mapsto \theta_fx \coloneqq \{f_n(x)\}_{n=1}^\infty\in \ell^p(\mathbb{N}), \quad \theta_g: \mathcal{D}(\theta_g) \ni x \mapsto \theta_gx \coloneqq \{g_n(x)\}_{n=1}^\infty\in \ell^p(\mathbb{N}). \end{align*} Inequality (1) is unexpectedly different from both bounded uncertainty principle \textit{[arXiv:2308.00312v1]} and unbounded uncertainty principle \textit{[arXiv:2312.00366v1]} for Banach spaces.

Sesquiterpene lactones (STLs) are a large group of terpenoids most commonly found in plants of the Asteraceae family, e. g. in chicory plants, displaying a wide range of interesting biological activities. However, further studies on the biological potential of chicory derived STLs and analogues are challenging as only four of these molecules are commercially available (as analytical standards), and to date there are no published or patented simple extraction-purification processes capable of large scale STLs isolation. In this work we describe a novel three-step large scale extraction and purification method for the simultaneous purification of 11,13-dihydrolactucin (DHLc) and lactucin (Lc) starting from a chicory genotype rich in these STLs and in the corresponding glycosyl and oxalyl conjugated forms. After a small-scale screening on 100 mg of freeze-dried chicory root powder, the best results were achieved with a 17 h water maceration at 30°C. With these conditions we managed to increase the content of DHLc and Lc, at the same time favouring the hydrolysis of their conjugated forms. On a larger scale, the extraction of 750 g of freeze-dried chicory root powder, followed by a liquid-liquid extraction step and a reversed-phase chromatography, allowed the recovery of 642.3 ± 76.3 mg of DHLc and 175.3 ± 32.9 mg of Lc. The two pure STLs were subsequently used in the context of semi-synthesis to generate analogues for biological evaluation as antibacterial agents. In addition, other described chicory STLs that are not commercially available were also synthesized or extracted to serve as analytical standards for the study. In particular, lactucin-oxalate and 11,13-dihydrolactucin-oxalate were synthesized in two steps starting from Lc and DHLc, respectively. On the other hand, 11β,13-dihydrolactucin-glycoside was obtained after a MeOH/H₂O (70/30) extraction, followed by a liquid-liquid extraction step and a reversed-phase chromatography. Together, this work will help facilitate the evaluation of the biological potential of chicory derived STLs and their semisynthetic analogues.

The paper is concerned with a class of stochastic differential equations in infinite dimensional Hilbert space with random coefficients driven by Teugel's martingales which are more general processes. and its optimal control problem. Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with L\'{e}vy processes (see Nualart and Schoutens). There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous dependence theorem of solutions combining with the parameter extension method. The second is to establish the stochastic maximum principle and verification theorem for our optimal control problem by the classicconvex variation method and dual technique.The third is to represent an example of a Cauchy problem for a controlled stochastic partial differential equation driven by Teugels martingales which our theoretical results can solve.

Prostate cancer (PCa) is the most diagnosed non-cutaneous cancer in men. Despite therapies such as radical prostatectomy, which is considered curative, distant metastases may form resulting in biochemical recurrence (BCR). This study used radiomic features calculated from multi-parametric magnetic resonance imaging (MP-MRI) to evaluate their ability to predict BCR and PCa presence. Data from a total of 279 patients, of which 46 experienced BCR, undergoing MP-MRI prior to surgery were assessed for this study. After surgery, the prostate was sectioned using patient-specific 3D-printed slicing jigs modeled using the T2-weighted imaging (T2WI). Sectioned tissue was stained, digitized, and annotated by a GU-fellowship trained pathologist for cancer presence. Digitized slides and annotations were co-registered to the T2WI and radiomic features were calculated across the whole prostate and cancerous lesions. A tree regression model was fitted to assess the ability of radiomic features to predict BCR, and a tree classification model was fitted with the same radiomic features to classify regions of cancer. We found that 10 radiomic features predict eventual BCR with an AUC of 0.97 and classifying cancer at an accuracy of 89.9%. This study showcases the application for a radiomics-based tool to screen for the presence of prostate cancer and assess patient prognosis, as determined by biochemical recurrence.

Power law relationships, which describe scaling relationships of data, are powerful information theoretic descriptive tools in many empirical contexts, including that of music. Zipf’s law (pink noise) describes the optimum case of a power law relation where observations are exactly inversely proportional to their rank. Descriptions that approximate a pink noise signature can be said to maximize the amount of information in a signal, and is thus suggestive of a richness of an understanding. This information density of pink noise signatures is not, however, necessarily a desirable quality for explanations in general, which, by definition, “flattens out” some data while highlighting others, ideally those most relevant to an interpretation. The privileging of data most relevant to comprehension corresponds to a red noise relationship, as opposed to the pink noise of Zipf’s law or the white noise of a description that highlights nothing in particular. Here, I explore and evaluate this concept of red noise explanations in the form of analyses of three comparable short piano works: Robert Schumann’s “Von fremden Ländern und Menschen” (no.1 from Kinderszenen op. 15, 1838), Frédéric Chopin’s Prelude op. 28 no. 20 (1838-9), and Felix Mendelssohn’s “Venetianisches Gondellied” (no. 6 from Lieder ohne Worte op. 19b, 1829-30).

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems).

The main goal of this article is the characterization of Herz-type Besov-Morrey spaces K˙p,qαN˙μ,rs and Triebel-Lizorkin-Morrey spaces K˙p,qαE˙μ,rs via ball means of differences, atomic, molecular and wavelet decompositions. There are provided necessary facts for implying these results, which can help to explore such spaces on different domains in further researches. Proposed spaces allow to extend the class of studying functions, containing Leray projection, heat semi-group and other operators, which can be helpful in exploring weak, strong and mild solutions of nonlinear partial differential equations.

For a nonzero normed linear space X‎, ‎we will define some different classes of fuzzy norms on X generated by linear and bounded linear functionals‎. ‎Also separate continuity of the elements of each class are investigated‎. ‎The aim of this research is to introduce a source of examples and counterexamples in the field of fuzzy normed spaces‎.

In 1999, Molodtsov initiated the theory of soft sets as a new mathematical tool for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied the notion of soft topological spaces, also defining and investigating many new soft properties as generalization of the classical ones. In this paper, we introduce the notions of soft separation between soft points and soft closed sets in order to obtain a generalization of the well-known Embedding Lemma to the class of soft topological spaces.

Background. To describe the characteristics of anterior mediastinal masses on conventional magnetic resonance imaging (MRI) and to assess the role of the Apparent Diffusion Coefficient (ADC) value in distinguishing benign from malignant mediastinal lesions. Methods. We conducted a retrospective cross-sectional study on 55 patients with anterior mediastinal mass who performed MRI before treatment. Biopsy and histopathological assessments were done after that. A radiologist evaluates the changes of signal intensity on these sequences: T1- weighted VIBE DIXON pre and post-contrast with Gadolinium, T2 HASTE, T2 TIRM, DWI/ADC, to determine the size, margin of the lesion, the presence of fat, cystic in it. ADCs values were calculated from the ADC maps which were constructed from b = 0 and b = 2000 Results. The study was composed of 55 patients, with 5 benign lesions and 50 malignant lesions. The ADCmean, ADCmedian, ADC10, and ADC90 in the histogram-based approach and hot-spot-ROI-based mean ADC for the malignant lesions was significantly lower than those found in benign lesions (P-value <0.05). The hot-spot-ROI-based mean ADC had the highest value in differentiation between benign and malignant mediastinal lesions, between group A (benign lesions, thymoma A, AB, B1) and group B (thymoma B2, B3 and other malignant lesions). The cut-off point of the ADC value differentiating malignant from benign mediastinal lesions was 1,17x10-3mm2/s with sensitivity of 80%, and specificity of 80%. The cut off point of the ADC value differentiating group A from group B was 0.99 x10-3mm2/s with sensitivity of 78,4%, and specificity of 88.9%. The cut-off point of the ADC value differentiating lymphoma from other malignant lesions was 0,91 x10-3mm2/s with sensitivity of 100%, and specificity of 60.5%. Conclusion. Diffusion-weighted MRI and measurement of ADC value in histogram-based approach and hot-spot-ROI-based mean ADC are very helpful in the differentiation between benign and malignant anterior mediastinal lesions.

Despite the abundance of tree diversity in the natural world, and generally high tree species richness in urban areas, urban forests continue to be dominated by a limited number of species. As socio-ecological systems, urban forests are shaped by historical and current management efforts and decision-making of a wide range of human actors. Drawing on past research, we offer a conceptual framework for describing the complex interactions among tree producers and consumers as trees are selected, grown, specified, and planted in private and public urban areas. We illustrate how multiple layers of selection criteria filter down the entirety of potential local tree diversity to a handful of commonly used and accepted tree species. We detail the actors and decision makers who impact tree composition and diversity across several land types. Finally, we identify research, education and outreach needs as they relate to creating more diverse and resilient urban forest ecosystems.

Eight lesions were analyzed using some algorithms of Intelligence Artificial: basal cell carcinoma (BCC), squamous cell carcinoma (SCC), melanoma (MEL), actinic keratosis (AK), benign keratosis (BKL), dermatofibromas (DF), melanocytic nevi (NV), and vascular lesions (VASC). This manuscript presents the possibility of using concatenated signatures (instead of images) obtained from different integral transforms, such as Fourier, Mellin, and Hilbert, to classify skin lesions. Eleven other Artificial Intelligence models were applied so that eight skin lesions could be classified by analyzing the particular signatures of each lesion. The database was randomly divided into 80%–20% for the training and test datasets images, respectively. The metrics that are being reported are accuracy, sensitivity, specificity, and precision. Each case was repeated 30 times to avoid bias, according to the central limit theorem in this work, and the average and ±standard deviation were reported. Although all the results were very satisfactory, the best average mark for the eight lesions analyzed was obtained using the Subspace KNN model, where the metrics for the test were 99.98% accuracy, 99.96% sensitivity, 99.99% specificity, and 99.95% precision.

Artistic image completion is fundamental for the preservation and restoration of invaluable art paintings and it has experienced significant progress through the implementation of deep learning methodologies. Despite these advancements, challenges persist, even with sophisticated approaches like Generative Adversarial Networks (GANs), particularly in achieving optimal results for high-resolution paintings. Small-scale texture synthesis and the inference of missing information from distant contexts present persistent issues, leading to distortions in lines and unnatural colors, especially in art paintings with complicated structures and textures. Concurrently, patch-based image synthesis has evolved by incorporating global optimization on the image pyramid to enhance structural coherence and details. However, methods relying on gradient-based synthesis encounter obstacles related to directionality, inconsistency, and the heavy computational burdens associated with solving the Poisson equation in non-integrable gradient fields. This paper introduces a groundbreaking approach, integrating Weighted Similarity-Confidence Laplacian Synthesis, to comprehensively address these challenges and advance the field of artistic image completion. This proposal addresses challenges not only in high-resolution artistic image completion but also makes a significant contribution to the broader field of patch-based synthesis by utilizing the Laplacian pyramid for enhanced edge-aware correspondence search. Experimental result confirms the effectiveness of our approach, offering promising outcomes for the preservation and restoration of art paintings with complicated details and irregular missing regions.

One of the most important applications in the wireless sensor networks (WSN) is to classify mobile targets in the monitoring area. In this paper, a multi-DBN weighted voting classification algorithm is proposed on the basis of the Deep Belief Network (DBN) classifier and combined with the idea of voting method, which is implemented on the nodes of the WSN monitoring system by means of "upper training, lower transplantation" appraoch. The performance of the algorithm is verified by using real-world experimental data, and the results show that the proposed method has a higher accuracy in classifying the target signal features, achieving an average classification accuracy of 84.63% across four different types of moving targets. The experiment reveals that the multi-DBN weighted voting algorithm enhances the target classification accuracy by approximately 5% in comparison to the single DBN classifier, but the memory and computation time required for the algorithm to run are also increased at the same time. Compared to the FFNN classifier, which exhibited the highest classification accuracy among the four selected methods, the algorithm achieves an improvement of approximately 8.8% in classification accuracy. However, it incurs greater time overhead to run.

The assessment outcomes of regional susceptibility to geological disasters can directly indicate the extent and intensity of risks within the study area, thus, providing targeted guidance for disaster management efforts. This study selects eight evaluation indicators, namely elevation, gradient, terrain relief, lithology of strata, normalized difference vegetation index, distance from the fault, distance from road, and distance from the river. The study focuses on Huize County in Yunnan Province as the research area, utilizing the certainty factor (CF) and random forest (RF) models for evaluating the susceptibility to geological disasters. The non-geological disaster points in the study area are determined using the deterministic coefficient prior model, and the deterministic coefficient values for each evaluation factor serve as the classification data for the random forest model. The optimal parameters for the random forest are selected through iterative calculations of bag error in PyCharm, while the weight of the evaluation factor is determined based on the ran-dom forest model with the optimal parameters. The results of geological disaster susceptibility zoning in Huize County are obtained by overlaying the weighted deterministic coefficients of each evaluation factor. The accuracy of the evaluation results is verified using zoning statistics and ROC curves with a test sample of 30% of the points. The results demonstrate the high accuracy of the model in evaluating the susceptibility to geological disasters in Huize County. Compared to the single deterministic coefficient model, this approach offers advantages in terms of reliability and accuracy. The evaluation results can serve as a scientific reference for related work in Huize County.

The airport ground handling services (AGHS) equipment supplier selection problem involves a safety guarantee on the part of the AGHS company that carries out the daily work. AGHS company can prevent aircraft damage and delays in airlines schedules, and ensure reliable and high-quality ground handling service. In our research, we developed an AGHS equipment supplier selection model based on the analytic hierarchy process and an AHP weighted fuzzy linear programming approach, and we solved the AGHS equipment supplier’s selection problem. The main objective of this article is to create an AHP and AHP-FLP decision model in order to help the AGHS company authorities select the best AGHS equipment supplier. The practical application in AGHS equipment supplier selection decisions can be interpreted as demonstrating that the proposed model provides knowledge and practical value for the AGHS industry.

Tail-biting convolutional codes extend the classical zero-termination convolutional codes: Both encoding schemes force the equality of start and end states, but under the tail-biting each state is a valid termination. This paper proposes a machine-learning approach to improve the state-of-the-art decoding of tail-biting codes, focusing on the widely employed short length regime as in the LTE standard. This standard also includes a CRC code. First, we parameterize the circular Viterbi algorithm, a baseline decoder that exploits the circular nature of the underlying trellis. An ensemble combines multiple such weighted decoders, each decoder specializes in decoding words from a specific region of the channel words' distribution. A region corresponds to a subset of termination states; the ensemble covers the entire states space. A non-learnable gating satisfies two goals: it filters easily decoded words and mitigates the overhead of executing multiple weighted decoders. The CRC criterion is employed to choose only a subset of experts for decoding purpose. Our method achieves FER improvement of up to 0.75dB over the CVA in the waterfall region for multiple code lengths, adding negligible computational complexity compared to the circular Viterbi algorithm in high SNRs.

In this paper, we introduce deboost, a Python library devoted to weighted distance ensembling of predictions for regression and classification tasks. Its backbone resides on the scikit-learn library for default models and data preprocessing functions. It offers flexible choices of models for the ensemble as long as they contain the predict method, like the models available from scikit-learn. deboost is released under the MIT open-source license and can be downloaded from the Python Package Index (PyPI) at https://pypi.org/project/deboost. The source scripts are also available on a GitHub repository at https://github.com/weihao94/DEBoost.

The rapid growth of urban areas has led to a decline in the amount of green space available to residents. This has a number of negative consequences for human health and well-- being. Green spaces provide a number of benefits for human health, including improved physical, mental, and social health. They also have a number of economic benefits, such as increased property values and reduced crime rates. Given the many benefits of green spaces, it is clear that they are essential for the health and well-being of urban residents. Policymakers and planners should prioritize the creation and preservation of green spaces in urban areas.

In this paper, we introduce a new class of open sets that is called is*-open set . Also, we present the notion of is*-continuous, is*-open, is*-irresolute, is*-totally continuous, and is-contra-continuous mappings, and we investigate some properties of these mappings. Furthermore, we introduce some is*-separation axioms, and is*-mappings are related with is*-separation axioms. . .

The previous two parts of the paper (correspondingly, https://philpapers.org/rec/PENFLT-2 and https://philpapers.org/rec/PENFLT-3) demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace of Hilbert space and especially its uniqueness can be unambiguously linked to that of partial algebra or incommensurability, or interpreted as a relation of the two dual branches of Hilbert arithmetic in a wide sense. The investigation of the last relation allows for FLT and Gleason’s theorem to be equated in a sense, as two dual counterparts, and the former to be inferred from the latter, as well as vice versa under an additional condition relevant to the Gödel incompleteness of arithmetic to set theory. The qubit Hilbert space itself in turn can be interpreted by the unity of FLT and Gleason’s theorem. The proof of such a fundamental result in number theory as FLT by means of Hilbert arithmetic in a wide sense can be generalized to an idea about “quantum number theory”. It is able to research mathematically the origin of Peano arithmetic from Hilbert arithmetic by mediation of the “nonstandard bijection” and its two dual branches inherently linking it to information theory. Then, infinitesimal analysis and its revolutionary application to physics can be also re-realized in that wider context, for example, as an exploration of the way for physical quantity of time (respectively, for time derivative in any temporal process considered in physics) to appear at all. Finally, the result admits a philosophical reflection of how any hierarchy arises or changes itself only thanks to its dual and idempotent counterpart.

Development and redevelopment are important drivers of tree removal and canopy loss in urban landscapes. Local ordinances are often used to curtail tree removal, but punitive regulations alone may not be enough to reduce urban tree canopy loss in land development. In Florida (US), efforts to balance trees and development have so far focused on fees and fines, but with a recent backlash against tree regulations and the fast pace of urban growth, we explored the possible role of incentives in urban tree policies. We interviewed 20 land developers across Florida to understand their perspectives on current barriers and potential incentives for tree preservation and planting. We collected data from developers, whose perspectives on tree preservation are often unknown or overlooked, despite their significant role in tree planting, removal, and retention in and around cities. Our results show that major barriers to tree preservation and planting include requirements to grade sites for stormwater management, site constraints, and monetary costs. Most developers did not know of any existing incentives beyond intrinsic motivations but said that financial incentives would be most appealing to them. Top incentive suggestions include increasing building density, reducing impact fees and tax liability, and changing tree mitigation policies. Another promising finding is that developers are willing to work with regulators to find solutions that benefit both parties. Future research should consider evaluating the level of support and viability of different incentives by gathering feedback from policymakers, land developers, and the public.

As urban development increases in density, the space to grow urban trees becomes more constrained. In heavily developed areas, small stature trees can be planted to reduce both above- and below-ground conflicts with infrastructure elements. However, even these species have their limits when placed in extremely confining conditions. In this study, we build on past work to determine the minimum planting widths of small stature urban trees. We found that species, stem diameter, and the height at which stem diameter measurements occurred were all strong predictors of trunk flare diameter (adjusted R² of 0.843). Additionally, we modelled the relationship between planting space and the presence or absence of hardscape conflicts – using the predictions derived from this effort to project the potential cost savings in two United States cities. Study results provide a guideline to create sufficient space for urban trees and minimize infrastructure damage and associated cost savings.

The administration of regional neuraxial analgesia for pain relief during labor is widely recognized as a safe and effective method involving medication delivery into the epidural or subarachnoid space in the lower back. This study proposes an innovative semantic image segmentation methodology emphasizing enhanced interpretability using convolutional Random Fourier Features and layer-wise weighted class-activation maps tailored explicitly for foot segmentation in regional analgesia monitoring. Namely, our contribution is twofold: i) a novel Random Fourier Features layer is introduced to deal with image data to enhance three well-known architectures (FCN, UNet, and ResUNet); ii) three novel quantitive measures are presented to evaluate the interpretability of a given deep learning model devoted to segmentation tasks. Our approach is rigorously evaluated on a demanding dataset of foot thermal images from pregnant women who received epidural anesthesia. Its small size and considerable variability characterize the dataset. Our validation results demonstrate that the proposed methodology not only achieves competitive foot segmentation performance but also significantly enhances the explainability of the process, rendering it well-suited for applications such as epidural insertion during labor.

Underwater robots often encounter the influence of confined underwater environments during underwater exploration. These environments include underwater caves, sunken ships, submerged houses, and pipeline structures. Robot positioning in these environments is strongly disturbed, leading not only to the failure of some commonly used positioning methods but also to an increase in errors in positioning systems that normally function well in open water. In order to overcome the limitations of positioning methods in underwater confined environments, researchers have studied different underwater positioning methods and selected suitable methods for positioning in such environments. These methods can achieve high-precision positioning without relying on assistance from other platforms, and are referred to as autonomous positioning methods. Autonomous positioning methods for underwater robots mainly include SINS/DR positioning and SLAM positioning. In addition, in recent years, researchers have also developed some bio-inspired autonomous positioning methods. This article introduces the applicable robot positioning methods and sensors in underwater confined environments and discusses the research directions of robot positioning methods in such environments.

We prove a quasi-pseudometric version of the strong Ekeland principle proved by P. Georgiev and T. Suzuki.

The theory says that number interacts with spaces based on the meaning of mathematics, this way it is possible to obtain numerical knowledge. The theory shows the possibility of using spaces relating to each other to explain the reasons why two even numbers form a pair, two odd numbers form a pair, an even and an odd number form an odd number, three odd numbers form an odd number, three even numbers form an odd number. one even, one odd and two evens form an odd, two odd and one even form a pair.

. In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions. We prove that our generalized affine functions have some similar properties with generalized convex functions. We present examples to show that our generalized affinenesses are different from one another, and also provide an example to show that our definition of presubaffinelikeness is non-trivial; presubaffinelikeness is the weakest generalized affineness introduced in this article. We work with optimization problems that are defined and taking values in linear topological spaces. We devote to the study of constraint qualifications, and derive some optimality conditions as well as a strong duality theorem. Our optimization problems have inequality constraints, equality constrains and abstract constraints; our inequality constraints are generalized convex functions and equality constraints are generalized affine functions.

The aim of this article is to make a multi-criteria analysis of various exhibition spaces of an originally non-exhibition character and to determine how these spaces affect the selection of works and the exhibition concept. The analysis is based on the exhibitions of art objects at collective exhibitions in unconventional architectural spaces: commercial, i.e. the modern office building of PBG Gallery Skalar Office Centre in Poznań, post-industrial i.e. in the former Zakłady Przemysłu Ziemniaczanego Lubanta S.A. and in the historic interior of the "U Jezuitów" Gallery of the Cultural Integration Centre in Poznań. The multi-criteria comparative analysis shows a variety of features of the studied spaces as well as the relationship between architecture and art and their mutual interaction. The participatory role of the non-exhibition space in the process of creating an exhibition and selecting works has been proven. It has also been confirmed that the presentation of works of art in originally non-exhibition spaces creates a new quality of the artwork. Unconventional architectural space, when used for the exhibition of works of art, expands and strengthens the area of ​​their influence through the interaction between the work and the architectural space. The specificity of the space adapted for exhibition needs, the presence and type of architectural details in the interior, the quantity and quality of light and its distribution in space, the volume and colour of the interior determine the exhibition space and influence the shape of the exhibitions organised and the reception of the artworks. The only condition for the change of the original function of an architectural space into that of an exhibition space is a coherent artistic vision of the creator. This should take into account the appropriate selection of the exhibited objects, where the process of searching for the relationship between architecture and art determines the features of the architectural space as integral components influencing the realisation of the exhibition .

We analyze the modular geometry of the variable exponent Lebesgue space L^p(.). We show that L^p(.) possesses a modular uniform convexity property. Part of the novelty is that the property holds even in the case supp(x) = ∞ . We present specific applications to fixed point theory. xÆΩ

Segmentation of a region of interest is an important pre-processing step for many colour image analysis techniques. Similarly segmentation of plant in digital images is an important preprocessing step in phenotying plants by image analysis. In this paper we present an analytical study to statistically determine the suitability of colour space representation of an image to best detect plant pixels and separate them from background pixels. Our hypothesis is that the colour space representation in which the separation of the distributions representing plant pixels and background pixels is maximized would be the best for detection of plant pixels. The two classes of pixels are modelled as a Gaussian mixture model (GMM). In our GM modelling we don't make any prior assumption about the number of Gaussians in the model. Rather a constant bandwidth mean-shift filter is used to cluster the data and the number of clusters and hence the number of Gaussians is automatically determined. Here we have analysed following representative colour spaces like $RGB$, $rgb$, $HSV$, $Ycbcr$ and $CIE-Lab$. This is because these colour spaces represent several other similar colour spaces and also an exhaustive study of all the colour space will be too voluminous. We also analyse the colour space feature from the two-class variance ratio perspective and compare the results of our hypothesis with this metric. The dataset for this empirical study consist of 378 digital images of plants and their manual segmentation. Dataset consist of various species of plants (arabidopsi, tobacco, wheat, rye grass etc.) imaged under different lighting conditions, indoor and outdoor, controlled and uncontrolled background. In results we obtain better segmentation of the plants in $HSV$ colour space, which is supported by its Earth mover distance (EMD) on the GMM distribution of plant and background pixels.

This study delves into the realm of heuristic evaluation within usability testing, focusing on refining and applying a tailored algorithm that simplifies the implementation of the Analytic Hierarchy Process for heuristic prioritization. Addressing the prevalent challenge of disparate evaluation methodologies and the absence of a standardized process in usability testing, our research introduces a novel method that leverages the Analytic Hierarchy Process alongside a bespoke algorithm. This algorithm utilizes transitive properties for pairwise comparisons, significantly reducing the evaluative workload. This innovative approach facilitates the estimation of heuristic relevance irrespective of the number of items per heuristic or the item scale and streamlines the overall evaluation process. In addition to rigorous simulation testing of the tailored algorithm, we applied our method in a practical scenario, engaging seven usability experts in evaluating a web interface. This empirical application underscored our method’s capacity to diminish the requisite comparison count and spotlight areas of improvement for critically weighted yet underperforming heuristics. The outcomes of this study underscore the efficacy of our approach in enhancing the efficiency and organization of heuristic evaluations, paving the way for more structured and effective usability testing methodologies in future research endeavors.