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We introduce a notion of pre-alternative algebra which may be seen as an alternative algebra whose product can be decomposed into two pieces which are compatible in a certain way. It is also the "alternative" analogue of a dendriform dialgebra or a pre-Lie algebra. The left and right multiplication operators of a pre-alternative algebra give a bimodule structure of the associated alternative algebra. There exists a (coboundary) bialgebra theory for pre-alternative algebras, namely, pre-alternative bialgebras, which exhibits all the familiar properties of the famous Lie bialgebra theory. In particular, a pre-alternative bialgebra is equivalent to a phase space of an alternative algebra and our study leads to what we called $PA$-equations in a pre-alternative algebra, which are analogues of the classical Yang-Baxter equation.

We show that Wise's power alternative is stable under certain group constructions, use this to prove the power alternative for new classes of groups, and recover known results from a unified perspective. For groups acting on trees, we introduce a dynamical condition that allows us to deduce the power alternative for the group from the power alternative for its stabilisers of points. As an application, we reduce the power alternative for Artin groups to the power alternative for free-of-infinity Artin groups, under some conditions on their parabolic subgroups. We also introduce a uniform version of the power alternative and prove it, among other things, for a large family of two-dimensional Artin groups. As a corollary, we deduce that these Artin groups have uniform exponential growth. Finally, we prove that the power alternative is stable under taking relatively hyperbolic groups. We apply this to show that various examples, including all free-by-$\mathbb{Z}$ groups and a natural subclass of hierarchically hyperbolic groups, satisfy the uniform power alternative.

In this paper, we introduce a novel generalization of the classical property of algebras known as "being alternative," which we term "partially alternative." This new concept broadens the scope of alternative algebras, offering a fresh perspective on their structural properties. We showed that partially alternative algebras exist in any even dimension. Then we classified middle $\mathbb C$-associative (noncommutative) algebras satisfying partial alternativity condition. We demonstrated that for any four-dimensional partially alternative real division algebra, one can select a basis that significantly simplifies its multiplication table. Furthermore, we established that every four-dimensional partially alternative real division algebra naturally gives rise to a real Lie algebra, thereby bridging these two important algebraic frameworks. Our work culminates in a description of all Lie algebras arising from such partially alternative algebras. These results extend our understanding of algebraic structures and reveal new connections between different types of algebras.

In this submission, I discuss my research on values, norms and practices of subcultures formed as an "alternative" to the dominant way of life. In particular, I explore how the Internet of Things (IoT) or intelligent agents relates to alternative forms of interaction or be understood and reconstructed through alternative concepts or frameworks. For the past three years I have been conducting fieldwork on communities pursuing alternative lifestyles. This work considers how those alternative lifestyles may contribute to an understanding of objects, spaces in future smart home. Through my fieldwork and research through design, I hope to offer an alternative vision to living with IoT and envision future domesticity in a unique and even groundbreaking way.

The algebraic and geometric classifications of complex $3$-dimensional right alternative and semi-alternative algebras are given. As corollaries, we have the algebraic and geometric classification of complex $3$-dimensional $\mathfrak{perm}$, binary $\mathfrak{perm}$, associative, $(-1,1)$-, binary $(-1,1)$-, and assosymmetric algebras. In particular, we proved that the first example of non-associative right alternative algebras appears in dimension $3;$ the first example of non-associative assosymmetric algebras appears in dimension $3;$ the first example of non-assosymmetric semi-alternative algebras appears in dimension $4;$ the first example of binary $(-1,1)$-algebras, which is non-$(-1,1)$-, appears in dimension $4;$ the first example of right alternative algebras, which is not binary $(-1,1)$-, appears in dimension $4;$ the first example of binary $\mathfrak{perm}$ non-$\mathfrak{perm}$ algebras appears in dimension $4.$ As a byproduct, we give a more easy answer to problem 2.109 from the Dniester Notebook, previously resolved by Shestakov and Arenas.

Alternative splicing allows an organism to make different proteins in different cells at different times, all from the same gene. In a cell that uses alternative splicing, the total length of all the exons is much shorter than in a cell that encodes the same set of proteins without alternative splicing. This economical use of exons makes genes more stable during reproduction and development because a genome with a shorter exon length is more resistant to harmful mutations. Genomic stability may be the reason why higher vertebrates splice alternatively. For a broad class of alternatively spliced genes, a formula is given for the increase in their stability.

The Alternative Hypothesis concerns a hypothetical and unlikely picture of how zeros of the Riemann zeta function are spaced which one would like to rule out. In the Alternative Hypothesis, the renormalized distance between nontrivial zeros is supposed to always lie at a half integer. It is known that the Alternative Hypothesis is compatible with what is known about the pair correlation function of zeta zeros. We ask whether what is currently known about higher correlation functions of the zeros is sufficient to rule out the Alternative Hypothesis and show by construction of an explicit counterexample point process that it is not. A similar result was recently independently obtained by T. Tao, using slightly different methods. We also apply the ergodic theorem to this point process to show there exists a deterministic collection of points lying in $\tfrac{1}{2}\mathbb{Z}$ which satisfy the Alternative Hypothesis spacing but mimic all statistics which are currently known about zeros of the zeta function.

Alphanumeric authentication routinely fails to regulate access to resources with the required stringency, primarily due to usability issues. Initial deployment did not reveal the problems of passwords, deep and profound flaws only emerged once passwords were deployed in the wild. The need for a replacement is widely acknowledged yet despite over a decade of research into knowledge-based alternatives, few, if any, have been adopted by industry. Alternatives are unconvincing for three primary reasons. The first is that alternatives are rarely investigated beyond the initial proposal, with only the results from a constrained lab test provided to convince adopters of their viability. The second is that alternatives are seldom tested realistically where the authenticator mediates access to something of value. The third is that the testing rarely varies the device or context beyond that initially targeted. In the modern world different devices are used across a variety of contexts. What works well in one context may easily fail in another. Consequently, the contribution of this paper is an "in the wild" evaluation of an alternative authentication mechanism that had demonstrated promise i

A groupoid is alternative if it satisfies the alternative laws $x(xy)=(xx)y$ and $x(yy)=(xy)y$. These laws induce four partial maps on $\mathbb{N}^+\times \mathbb{N}^+$, $(r,\,s)\mapsto (2r,\,s-r)$, $(r-s,\,2s)$, $(r/2,\,s+r/2)$, $(r+s/2,\,s/2)$ that taken together form a dynamical system. We describe the orbits of this dynamical system, which allows us to show that $n$th powers in a free alternative groupoid on one generator are well-defined if and only if $n\le 5$. We then discuss some number theoretical properties of the orbits, and the existence of alternative loops without two-sided inverses.

The suggested alternative cosmology is based on the idea of barion symmetric universe, in which our home universe is a representative of multitude of typical matter and antimatter universes. This alternative concept gives a physically reasonable explanation of all major problems of the Standard Cosmological Model. Classification Code MSC: Cosmology 524.8 Key words: standard cosmological model, alternative cosmology, barionic symmetry, typical universe, quasars, cosmic rays.

The theory of unified product and extending structures for alternative and pre-alternative algebras are developed. It is proved that the extending structures of these algebras can be classified by using some non-abelian cohomology and deformation map theory.

We introduce the concept of braided alternative bialgebra. The theory of cocycle bicrossproducts for alternative bialgebras is developed. As an application, the extending problem for alternative bialgebra is solved by using some non-abelian cohomology theory.

A new version of Farkas lemma of alternative linear systems is proposed. One and the same matrix $A$ and vector $b$ have always been used in alternative linear systems. The paper shows a different way of alternative systems involving application of different matrices with various dimensions, which can be advantageous from computational point of view.

We address neutron stars and black holes in alternative gravities, after recalling their basic properties in General Relativity. Among the plethora of interesting alternative gravities we here focus on an interesting set of scalar-tensor theories. We discuss the phenomenon of spontaneous scalarization, that is matter induced for neutron stars and curvature induced for black holes. Along with other relevant physical properties, we address the quasi-normal modes of these compact objects. In particular, we consider \textit{universal relations} of neutron stars to largely reduce the dependence on the equation of state, and we briefly address the shadow of black holes.

We prove the Girth Alternative for a sub-class of the HNN extensions of finitely generated groups. We also produce counterexamples to show that beyond our class, the alternative fails in general.

A theorem of Cantat and Urech says that an analog of the classical Tits alternative holds for the group of birational automorphisms of a compact complex Kaehler surface. We established in our previous paper the following Tits-type alternative: if X is a toric affine variety and G is a subgroup of Aut(X) generated by a finite set of unipotent subgroups normalized by the acting torus then either G contains a nonabelian free subgroup or G is a unipotent affine algebraic group. In the present paper we extend the latter result to any group G of automorphisms of a complex affine surface generated by a finite collection of unipotent algebraic subgroups. It occurs that either G contains a nonabelian free subgroup or G is a metabelian unipotent algebraic group.

Although altmetrics and other web-based alternative indicators are now commonplace in publishers' websites, they can be difficult for research evaluators to use because of the time or expense of the data, the need to benchmark in order to assess their values, the high proportion of zeros in some alternative indicators, and the time taken to calculate multiple complex indicators. These problems are addressed here by (a) a field normalisation formula, the Mean Normalised Log-transformed Citation Score (MNLCS) that allows simple confidence limits to be calculated and is similar to a proposal of Lundberg, (b) field normalisation formulae for the proportion of cited articles in a set, the Equalised Mean-based Normalised Proportion Cited (EMNPC) and the Mean-based Normalised Proportion Cited (MNPC), to deal with mostly uncited data sets, (c) a sampling strategy to minimise data collection costs, and (d) free unified software to gather the raw data, implement the sampling strategy, and calculate the indicator formulae and confidence limits. The approach is demonstrated (but not fully tested) by comparing the Scopus citations, Mendeley readers and Wikipedia mentions of research funded by W

This paper emerged as a result of tackling the following three issues. Firstly, we would like the well known embedding of bicategories into pseudo double categories to be monoidal, which it is not if one uses the usual notion of a monoidal pseudo double category. Secondly, in \cite{Gabi} the question was raised: which would be an alternative notion to intercategories of Grandis and Paré, so that monoids in Böhm's monoidal category $(Dbl,\ot)$ of strict double categories and strict double functors with a Gray type monoidal product be an example of it? We obtain and prove that precisely the monoidal structure of $(Dbl,\ot)$ resolves the first question. On the other hand, resolving the second question, we upgrade the category $Dbl$ to a tricategory $\DblPs$ and propose %an alternative definition of intercategories as to consider internal categories in this tricategory. %, enabling monoids in $(Dbl,\ot)$ to be examples of this gadget. Apart from monoids in $(Dbl,\ot)$ - more importanlty, weak pseudomonoids in a tricategory containing $(Dbl,\ot)$ as a sub 1-category - most of the examples of intercategories are also examples of this gadget, the ones that escape are those that rely on la

The dominant contributions from a discrete gravitational interaction produce the standard potential as an effective continuous field. The sub-dominant contributions are, in a first approximation, linear on $n$, the accumulated number of (discrete) interaction events along the test-body trajectory. For a nearly radial trajectory $n$ is proportional to the transversed distance and its effects may have been observed as the Pioneer anomalous constant radial acceleration, which cannot be observed on the nearly circular planetary orbits. Here we give calculation details of the alternative II, discussed in gr-qc/0106046.

We look at the equilibrium of a Brownian particle in an inhomogeneous space following the alternative approach proposed in ref.[1]. We consider a coordinate dependent damping that makes the stochastic dynamics the one with multiplicative noise. Here we show that the mapping to an additive noise gives the equilibrium distribution of the generalized Langevin dynamics of a particle with mass. The procedure does not need inclusion of any ad hoc current cancelling term in the Langevin dynamics. The result shows a modified Maxwell-Boltzmann distribution with a damping dependent amplitude.