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Denote by H the set of all quaternions. We are interested in the group U (1 , 1 ; H) , which is a subgroup of 2 × 2 quaternionic matrix group and is sometimes called Sp(1, 1). As well known, U (1 , 1 ; H) corresponds to the quaternionic Möbius transformations on the unit ball in H . In this article, some similarity invariants on U (1 , 1 ; H) are discussed. Our main result shows that each matrix T ∈ U (1 , 1 ; H) , which corresponds to an elliptic quaternionic Möbius transformation g T (z) , could be U (1 , 1 ; H) -similar to a diagonal matrix. Moreover, one can see that each elliptic quaternionic Möbius transformation is quaternionic Möbius conjugate to a bi-rotation, where a bi-rotation means a map z → p · z · q - 1 for some p , q ∈ H with | p | = | q | = 1 . [ABSTRACT FROM AUTHOR]

This is the last one of three successive articles by the authors on matrix-weighted Besov-type and Triebel–Lizorkin-type spaces B ˙ p , q s , τ (W) and F ˙ p , q s , τ (W) . In this article, the authors establish the molecular and the wavelet characterizations of these spaces. Furthermore, as applications, the authors obtain the optimal boundedness of trace operators, pseudo-differential operators, and Calderón–Zygmund operators on these spaces. Due to the sharp boundedness of almost diagonal operators on their related sequence spaces obtained in the second article of this series, all results presented in this article improve their counterparts on matrix-weighted Besov and Triebel–Lizorkin spaces B ˙ p , q s (W) and F ˙ p , q s (W) . In particular, even when reverting to the boundedness of Calderón–Zygmund operators on unweighted Triebel–Lizorkin spaces F ˙ p , q s , these results are still better. [ABSTRACT FROM AUTHOR]

Trace detection in tunnel faces is critical for preventing failures such as spalling in tunnel excavations. This paper proposes a novel method, referred to as the Roughness-CANUPO (R–C) Method, for the automatic detection of these traces in 3D point clouds obtained from tunnel faces, in which its combines roughness analysis with the CANUPO machine learning algorithm to improve the accuracy and efficiency of trace detection. In this study, images were collected from six sites and point cloud data of 6 sites were obtained by 3D reconstruction. Points representing rock masses in the collected 3D point cloud data can be filtered by roughness analysis in the R–C methods. Roughness analysis can not only significantly reduce the analysis time of CANUPO machine learning, but also increase the accuracy of CANUPO analysis. In this paper, the local neighbourhood radius (LNR) and filtering ratio optimized in the roughness analysis and the roughness for filtering discontinuities were evaluated. The filtered point cloud data automatically extract only the trace point cloud by the CANUPO classifier. The extracted trace was projected onto the original data to accurately designate the location of the trace. Conducting the R–C method yields a significant result regarding discontinuity traces classification by reaching the level of accuracy ranging from 95.9% to 98.9%. [ABSTRACT FROM AUTHOR]

A method for banknote identification has been developed. As a prerequisite for this process, an ATM stores records captured from accepted banknotes, including customer's information for identification. The proposed method is implemented when a counterfeit banknote is detected. The ATM identifies a record corresponding to the counterfeit banknote among the stored records, assisting in the identification of the customer who used it. This identification is carried out by exploiting characteristic differences between counterfeit and genuine banknotes. These differences are defined in terms of positions and magnitudes of variations. An experiment using simulated banknotes was conducted to assess the effectiveness of the proposed method. Additionally, another experiment involving digitally synthesized banknotes was conducted to determine the performance limits of the proposed method. [ABSTRACT FROM AUTHOR]

Let \alpha be a non-zero algebraic number. Let K be the Galois closure of \mathbb {Q}(\alpha) with Galois group G and \bar {\mathbb {Q}} be the algebraic closure of \mathbb {Q}. In this article, among the other results, we prove the following. If f\in \bar {\mathbb {Q}}[G] is a non-zero element of the group ring \bar {\mathbb {Q}}[G] and \alpha is a given algebraic number such that f(\alpha ^n) is a non-zero algebraic integer for infinitely many natural numbers n, then \alpha is an algebraic integer. This result generalises the result of Polya [Rend. Circ Mat. Palermo, 40 (1915), pp. 1–16], Corvaja and Zannier [Acta Math. 193 (2004), pp. 175–191] and Philippon and Rath [J. Number Theory 219 (2021), pp. 198–211]. We also prove the analogue of this result for rational functions with algebraic coefficients. Inspired by a result of B. de Smit [J. Number Theory 45 (1993), pp. 112–116], we prove a finite version of the Polya type result for a binary recurrence sequences of non-zero algebraic numbers. In order to prove these results, we apply the techniques of Corvaja and Zannier along with the results of Kulkarni et al. [Trans. Amer. Math. Soc. 371 (2019), pp. 3787–3804], which are applications of the Schmidt subspace theorem. [ABSTRACT FROM AUTHOR]

In this paper, we define extensions of the classical eigenvalues of the matrix A ∈ Mm(C). These extensions are eigenvalues matrices for the block matrix A ∈ Mm(Mn), where Mm(Mn) is the set of all m×m block complex matrices with each block in Mn(C), they are.....Among other equalities and inequalities, we prove equalities which relate our new definitions with tr1(A) and tr2(A) as follows,... These relations are extensions of the classical relation tr(A) = Σmh=1λh(A), where A ∈Mm(C). Several new relations and properties of our new definitions are also given. [ABSTRACT FROM AUTHOR]

Background: Tuberculosis (TB) continues to be a major cause of morbidity and mortality worldwide. The main strategy to fight the pandemic is the development of rapid, accurate diagnostic tests, which helps to reduce the time for initiation of therapy. In 2010, WHO recommended the use of Xpert Mycobacterium tuberculosis/rifampicin (MTB/RIF) (G4), which is a cartridge-based semi-automated nucleic acid amplification test (NAAT) as a primary test with an aim to improve the detection of MTB. Later on, to improve the diagnostic efficacy, the new and improved cartridges called Xpert Ultra were introduced in 2017. MATERIALS AND METHODS: One thousand and sixty-nine clinical samples were utilized for the study for microscopy, culture, and NAATs (Xpert MTB/RIF G4 and Ultra). The samples were randomly allocated. Sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) were calculated while assuming trace results as positive and negative in two separate scenarios. Results: The sensitivity of Xpert MTB/RIF Ultra cartridge was higher (100%) than Xpert MTB/RIF G4 cartridge (95.23%) and the specificity of Ultra cartridge was lower (71.79%) when compared to G4 cartridge (91.63%). However, the specificity of Xpert Ultra cartridge improved by reclassifying the “trace” interpretation as negative (89.1%). The NPV was 100% and 99.09% for Xpert Ultra cartridge and the Xpert G4 cartridge, respectively, and did not change by reclassifying the “trace” interpretation as negative. In contrast, the PPV varied greatly between the two tests, 26.66% for Xpert Ultra cartridge and 66.66% for Xpert G4 cartridge. The PPV of Xpert Ultra cartridge was improved to 48.48% by including “trace” samples in the negative pool. Conclusion: Xpert Ultra and G4 shows good performance as a first line diagnostic test. Caution should be exercised when interpreting ‘trace’ results in a country like India without parallel confirmatory tests like microscopy and culture. Data is limited on this newly incorporated value assigned in the automated report. Conducting further studies on results interpreted as ‘trace’ will help in improving the guidelines and as well as utilisation of such tests.

Let F be the finite field of order q and M (n , r , F) be the set of n × n matrices of rank r over the field F. For α ∈ F and A ∈ M (n , F) , let Z A , r α = { X ∈ M (n , r , F) | Tr (A X) = α }. In this article, we solve the problem of determining the cardinality of Z A , r α. We also solve the generalization of the problem to rectangular matrices. [ABSTRACT FROM AUTHOR]

We introduce neutrosophic rhotrices, which serve as a novel extension of neutrosophic matrices. The primary objective is to establish the foundational structure for neutrosophic rhotrices and to define crucial operations that can be performed on them. We explore the concept of neutrosophic rhotrices in depth, outlining the fundamental operations necessary for their effective manipulation. Furthermore, we investigate the essential properties of neutrosophic rhotrices utilizing these newly established operations. In addition, we provide an algorithm designed to enhance decision-making processes in medical diagnostics, supported by an illustrative example to clarify its application. [ABSTRACT FROM AUTHOR]

Passive safety systems are integrated into the latest generation of Light Water Reactors (LWRs), including small modular reactors. This paper employs the US-NRC TRACE thermal hydraulic code to examine the performance of a passive safety condenser known as SACO, designed to serve as the ultimate heat sink for dissipating decay heat during accident scenarios. The TRACE model is constructed with reference to the PKL/SACO test facility. The safety condenser (SACO) is interconnected with the PKL facility via the secondary side of steam generator 1, effectively serving as a third natural circulation cooling loop during accident scenarios. In the present research, the thermal-hydraulic behavior of the PKL facility is investigated in the presence of the SACO passive safety system during an extended SBO with Loss of AC Power accident scenario. This SBO can be categorized into three distinct phases depending on the activation of the SACO system and the refilling process of the SACO pool. The first phase is depressurizing using primary and secondary relief valves, the second phase is cooling down using SACO system, and the third phase is the refilling of SACO pool. The findings indicate that the SACO system effectively manages to dissipate all decay heat, even though there is temporary evaporation of the SACO water pool. Furthermore, this study provides sensitivity analysis for the assessments of system codes on the selection of maximum time step.

Abstract–In this paper, based on the classifications of Kn-simple groups for n≤6 and under the case that every maximal subgroup has a π-nilpotent trace, we obtained the necessary and sufficient conditions on solvable groups and proved that two unsolvable problems involving groups, rings and fields are true. [ABSTRACT FROM AUTHOR]

In this paper, three discrete transforms related to vector spaces over finite fields are studied. For our purposes, and according to the properties of the finite fields, the most suitable transforms are as follows: for binary fields, this is the Walsh–Hadamard transform; for odd prime fields, the Vilenkin–Chrestenson transform; and for composite fields, the trace transform. A factorization of the transform matrices using Kronecker power is given so that the considered discrete transforms are reduced to the fast discrete transforms. Examples and applications are also presented of the considered transforms in coding theory for calculating the weight distribution of a linear code. [ABSTRACT FROM AUTHOR]

Let A and B be n × n positive semidefinite matrices, and let | | · | | 2 be the Hilbert-Schmidt norm. Bhatia and then Hayajneh and Kittaneh, using different techniques, proved that | | A v B 1 - v + B v A 1 - v | | 2 ≤ | | A + B | | 2 for v ∈ 1 4 , 3 4 , which gives an affirmative answer to an open problem posed by Bourin for the special case of the Hilbert–Schmidt norm. In this paper, we prove a general unitarily invariant norm inequality from which we obtain a new proof of the above Hilbert–Schmidt norm inequality. We also prove that if r ≥ 1 , then | | | A v B 1 - v + B v A 1 - v | | | ≤ | | | (A 1 / r + B 1 / r) r | | | for 1 2 r ≤ v ≤ 2 r - 1 2 r , where | | | · | | | denotes any unitarily invariant norm. [ABSTRACT FROM AUTHOR]

A new ichnotaxon, Ambulopisces voigti (ichnogen. et ichnosp. nov.), from the early Permian (Wolfcampian) Robledo Mountains Formation (Hueco Group) of south-central New Mexico, is described and shown to represent a fish walking on a muddy substrate. A. voigti is a compound ichnotaxon comprising alternating left and right pectoral fin impressions that show the walking behaviour plus a superimposed sinusoidal caudal fin drag that can be assigned to Undichna. The pectoral fin impressions are surrounded by expulsion rims, which show that the fins were weight-bearing; these are larger posteriorly where sediment was pushed up by the propulsive motion of the fin. The shape of the expulsion rims thus indicates the direction of travel. Propulsion was accomplished by alternately pressing the pectoral fins into the substrate and flexing the body to bring the opposing pectoral fin and the body forward. The identity of the tracemaker is uncertain, but it was a small, low-profile fish whose pectoral fins spanned only ~ 60 mm. The proximity of the pectoral fin bases to the centerline of the trace does not support a lobe-finned fish as the tracemaker. [ABSTRACT FROM AUTHOR]

In this paper we will apply the tensor and its traces to investigate the spectral characterization of unicyclic graphs. Let G be a graph and Gm be the m-th power (hypergraph) of G. The spectrum of G is referring to its adjacency matrix, and the spectrum of Gm is referring to its adjacency tensor. The graph G is called determined by high-ordered spectra (DHS, for short) if, whenever H is a graph such that Hm is cospectral with Gm for all m, then H is isomorphic to G. In this paper we first give formulas for the traces of the power of unicyclic graphs, and then provide some high-ordered cospectral invariants of unicyclic graphs. We prove that a class of unicyclic graphs with cospectral mates is DHS, and give two examples of infinitely many pairs of cospectral unicyclic graphs but with different high-ordered spectra. [ABSTRACT FROM AUTHOR]

I respond to the provocation of this issue focusing on the action [reading] to theorize it in its openness to what is not present, as the texts are never present to be read. Using the Derridian quasi-concepts of trace and specter, I understand "reading" as a long exercise of responding to the otherness of the text. I defend that it is necessary to refuse the representational tradition of reading, to continuously deconstruct the metaphysical colonial legacy of what does it mean to read. Mostly, I argue that this process requires more and not less readings of what one seeks to deconstruct—a long preparation that is the research-event. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the traces of the adjacency tensor of uniform hypergraphs (simply called the traces of hypergraphs). We give new expressions for the traces of hypertrees and linear unicyclic hypergraphs by the weight function assigned to their connected sub-hypergraphs, and present some perturbation results for the traces of a hypergraph when its structure is locally changed. As an application we determine the unique hypertree with maximum Estrada index among all hypertrees with perfect matchings and given number of edges, and the unique unicyclic hypergraph with maximum Estrada index among all unicyclic hypergraph with girth 3 and given number of edges. [ABSTRACT FROM AUTHOR]

For 1 ≤ p < ∞ , let L p (M , τ) be the non-commutative L p -space associated with a von Neumann algebra M , where M admits a normal semifinite faithful trace τ . Using the trace τ , Banach duality formula and Gâteaux derivative, this paper characterizes an element a ∈ L p (M , τ) such that ‖ a ‖ p = inf { ‖ a + b ‖ p : b ∈ B p } , where B p is a closed linear subspace of L p (M , τ) and ‖ · ‖ p is the norm on L p (M , τ) . Such an a is called B p -minimal. In particular, minimal elements related to the finite-diagonal-block type closed linear subspaces B p = ⨁ i = 1 ∞ e i S e i (converging with respect to ‖ · ‖ p ) are considered, where { e i } i = 1 ∞ is a sequence of mutually orthogonal and τ -finite projections in a σ -finite von Neumann algebra M , and S is the set of elements in M with τ -finite supports. [ABSTRACT FROM AUTHOR]

The article examines the peculiarities of the emergence and formation of methods of forensic investigation, which over time, in the 19th century, took shape in the science of forensics. To solve the problems, the authors used several methods, both general scientific and special. Among them: formallegal, comparative-legal, historical-legal, dialectical, historical, systemic, hermeneutic, etc. The authors identified the main, in their opinion, stages of the development of criminology in Ukraine, starting with the formation of the Old Russian state. The first steps of the creation and implementation of forensic methods during the investigation of crimes, which were enshrined in the most famous monuments of law – «Laws of King Hammurabi», «Laws of the XII Tables», Byzantine legal collections, «Ruska Pravda», «Lithuanian Statutes», «The rights by which the Little Russian people are judged.» The article proves that the formation of individual manifestations of forensic research in Ukrainian lands during the Middle Ages and the first centuries of modern history was based on world experience in this area, as well as on the idea of justice, the need to restore law and order. It is emphasized that the formation of ideas about the methods of forensic research that appeared in Ukraine is connected with the genesis of the Ukrainian legal system and turned, over time, into one of its institutions. The authors suggest that, in contrast to the application of punishment, which had a class character, the organization of forensic investigations established the truth and therefore did not depend on the class affiliation of the participants in legal relations. The opinion that both in ancient times and at the beginning of the Middle Ages, forensic methods were closely intertwined with the elements of the investigative process, within which they were actually applied, is substantiated. It was established that the crippling forms of punishment, which were applied by court decision, were also intended to «emphasize» the identity of the criminal, to single him out in order to facilitate the search in case of repeated offenses. The authors concluded that the legal regulation of forensic research methods became a guarantee of their development, distribution and transformation, over time, into an independent science. [ABSTRACT FROM AUTHOR]

The soil–plant-animal continuum represents an evolving realm in biological research that’s why this study was undertaken in the middle Gangetic plain region of India. Trace and ultra-trace elements were analyzed in 100 soil samples, 147 feed and fodder samples, as well as 69 blood and 127 hair samples with the help of inductively coupled plasma optical emission spectroscopy (ICP-OES). The levels of trace and ultra-trace elements in the soil were significantly higher than those in the feed, and similarly, the concentrations in the feed were notably higher than those in the blood of dairy cattle. Blood and hair samples from the cattle showed deficiencies in copper (Cu) and manganese (Mn), with reaching approximately 20% and 50%, respectively. Correlation analysis indicated significant (P < 0.05) associations between the trace and ultra-trace elements in plants and the corresponding elements found in cattle's hair, specifically for iron (Fe) and molybdenum (Mo). Conversely, a significant (P < 0.05) negative correlation was observed between soil composition and cattle's blood, while a positive correlation was evident only in the case of silver content between plant and cattle's hair. Regression analyses revealed positive linear relationships between minerals in soils and plants, as well as between plants and cattle. However, the correlation coefficients were statistically insignificant. The regression equations established to predict mineral concentrations in cattle based on soil and plant mineral contents indicated a positive relationship for both trace and ultra-trace elements, suggesting the potential to measure the mineral status in dairy cattle through this approach. [ABSTRACT FROM AUTHOR]

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Let A and B be complex unital Banach algebras, and let φ , ψ : A → B be surjective mappings. If A is semisimple with an essential socle and φ and ψ together preserve the invertibility of linear pencils in both directions, that is, for any x , y ∈ A and λ ∈ C , λ x + y is invertible in A if and only if λ φ (x) + ψ (y) is invertible in B , then we show that there exists an invertible element u in B and a Jordan isomorphism J : A → B such that φ (x) = ψ (x) = u J (x) for all x ∈ A. [ABSTRACT FROM AUTHOR]

In decades since 11 September 2001 (9/11), surveillance and policing within the United States have increased manifold and, with them, protests against the systemic racism and classism embedded in these practices. These practices go back beyond the 21st century—these modes of policing, power, and protests against them are not new. Due to urban spaces' concentration of political, economic, and social power and the sheer density of people, they can quickly take on material and symbolic importance that can last for centuries. As public protests increase, so do countermeasures from those wielding power in the forms of both formal and informal policing and surveillance. These policing measures also leave material traces in the landscape, working to create a palimpsest of trauma across urban terrains. The lineage of a surveillance landscape as seen in policing, power, and protest in Lower Manhattan, will be explored through a documentary archaeological approach to examine the residual trauma left in public spaces. [ABSTRACT FROM AUTHOR]

Density wave oscillation (DWO) is one of the most extensively studied dynamic two-phase flow instabilities. The accurate prediction of these phenomena is important to ensuring safety in two-phase flow systems, such as boiling water reactors (BWRs). Recent reactor power uprates have led to the need for more accurate simulations at the system scale. For reactor licensing, the thermal-hydraulic computational code TRACE, developed by the U.S. Nuclear Regulatory Commission, is used for best-estimate predictions of light water reactors. One BWR power uprate condition of recent interest is the Maximum Extended Load Line Limit Analysis Plus, or MELLLA+, which allows BWRs to operate at lower core flow rates while maintaining the same power levels. Experiments performed at the Karlstein thermal-hydraulic test facility (KATHY) have shown that an anticipated transient without scram while operating under these conditions can lead to the development of DWOs. This technical note assesses the capability of TRACE V5P7 to simulate DWO onset and development by comparison to the KATHY experimental data under natural circulation, focusing only on the thermal-hydraulic mechanisms. This study shows the analysis of DWO development from this data set, which utilized electrically heated fuel rods with a nonuniform axial power profile in a full-scale BWR rod bundle. The developed TRACE model is shown to be capable of producing DWO-type instability under the experimental conditions, while also allowing for an expanded parametric study on factors impacting stability. [ABSTRACT FROM AUTHOR]

Levinas mainly deals with the notion of eschatology in the preface of Totalité et infini (1961). There it appears in the context of his agreement with an entire tradition of philosophers claiming that the very nature of being is one of violence and war, which becomes manifest in the pervasive waging of political battles and wars. He further contends that a conception of morality based on the “pure subjectivism of the I” is powerless to shield humankind against such violence. The alternative he offers to such an impotent morality is an ethics of alterity. Eschatology is Levinas’s answer to how such an ethics of alterity would be capable of insulating humankind against calculative reason and the pressures of politics and war. To understand how eschatology succeeds in doing so and how Levinas fills in the notion, I argue that it should be understood within the context of his conceptualisation of time. Levinas offers novel analyses of the forms and the work of time. Time, in Levinas, is the very inner structure of an existent’s movement of existing – I refer in this regard to the inherent chronological inconsistency of the human condition. In Levinas’s ethical metaphysics this inherent chronological inconsistency is theorised as the other (autre) within the self, an affective infection that dates back to a past that has never been present – it hails from the diachronic time of the Other – and is opened to the future, “to the newness of the unknown”. While this past is impossible to grasp, it nevertheless concerns me. I cannot remain unaffected in relation to it; it has left a trace. This alterity within the self becomes manifest as an inherent Desire for time, time that can only be given by the other person, which for Levinas is the Other (l’Autrui). This means that the singular time of my being is not yet time, does not yet have time, but the singular I bears an inherent Desire for time within. This Desire for time, then, emanates from the inherent chronological inconsistency which typifies the existent being “out of sync” with itself, a diastasis or a “standing apart from itself”. To be sure, this Desire is not a need to be filled, but as Desire, it is essentially insatiable. This Desire conquers the ecstatic time of need and satisfaction and the inevitable return to the self, the collapse back upon oneself that follows when needs are satiated, and the return of the unbearable heaviness of being that it signals. The early Levinas (De l’évasion, 1935) was looking for an escape from this irremediable Being. Only four decades later in Autrement qu’être ou au-delà de l’essence (1974) will Levinas come to fully plot out “a new path out of being,” a temporal path that he started to chart in Le temps et l’ autre (1948), which forges a fundamental link between time and ethics. The time that the future brings is not merely the recurrence of the present instant or its continuation, but the possibility of another instant or a new beginning. How can an existent in the instant recommence otherwise? The coming of the future announces another original instant that cannot be approached but that comes; that cannot be assumed, since it appears as an epiphany. The existent is able to welcome the absolutely strangeness of the epiphany of the future because of the inherent susceptibility to fraternity and sociality, which is made possible by time. This, however, is not time that the existent has like a possession but a capacity to welcome time that springs from an existential chronological inconsistency – a being temporally out of joint. To further specify, this “capacity” is not a power that the individual instant is endowed with. Quite to the contrary, faced with the radical strangeness of the future, with the alterity of the face of the Other, the existent is reduced to a “radical passivity.” Passivity is the radix or root of ethical agency. The capacity that time gives, is the capacity for generosity, the power to be able to give of the riches accumulated. This is not to turn away from one’s egotistical selfish life once and for all, but a being turned to be able to welcome the Other without being obliterated in the face of an absolute Mystery. The instant as an interruption announces the possibility of a new beginning, which is not the effacement of the past, but the pardon that purifies the past and the injustices committed. Pardon consists in a retroactive action that inverts the natural temporal order of things and implies the “reversibility of time”. Now the past instant has not passed but can be lived again, differently. In Levinas we find a non-teleological conception of time. Truth, Levinas contends, requires both an infinite time and a completed time conceived as “messianic time”. Messianic time, more precisely, may be conceived as the “extreme vigilance of the messianic consciousness”, since it is only such vigilant consciousness that can protect us against the revenge of evil – which infinite time cannot do. This notion of “messianic consciousness” is encapsulated in Levinas’s conceptualisation of eschatology, which is the infinity beyond totality or beyond history, without denying history. The eschatological is not realised at the end of time but rather in each instant in which our responsibility vis-à-vis the Other is realised. If this responsibility exempts us from the jurisdiction of history and the future, salvation is not to be found at the end of history but remains at each moment possible. When Levinas speaks of eschatology in Totalité et Infini he does not refer to a doctrine but to a vision: “the eschatological vision” that consummates moral experience. It is not a spiritual relationship; it leads to action. To see (envision) is already to act. This action is evoked in feeling responsible in the face of the future one hopes for others. The future one hopes for others – a better future – is the eschatological vision realised in the eruption of the present as a purified past. [ABSTRACT FROM AUTHOR]

Via inequalities for the spread of a matrix we characterize the trace on the full matrix algebra among all positive linear functionals with , where is the unit of and . We also present three characterizations of the trace in this class of functionals for all . [ABSTRACT FROM AUTHOR]

It is shown how certain recent results in the theory of determinants and traces can be applied to obtain new theorems on the distribution of eigenvalues of nuclear operators on Banach spaces and to prove the equality of the spectral and nuclear traces of such operators. As an example, we consider a new class of operators: the class of generalized Lapresté nuclear operators. [ABSTRACT FROM AUTHOR]

The article shows how Yu. N. Bartenev influenced the work of poetess A. I. Gotovtseva. Bartenev appears as a bright, multifaceted, and contradictory person. The article proves that Gotovtseva’s communication with Bartenev became one of the significant factors in her creative self-determination and artistic development. The poetic messages of Gotovtseva to Bartenev were created at different times but indicate that the mentor’s influence on the poetess has not weakened over the years. The article notes that Bartenev’s trace in Gotovtseva’s poetry is also represented in latent form. As an example of such a representation, we consider Gotovtseva’s poems, which refer to the personality and work of A. P. Khvostova, who is part of Bartenev’s closest spiritual circle (“Khvostova, the new Prometheus...” and “Fireplace”). The article demonstrates that Bartenev’s influence largely shaped Gotovtseva’s literary taste and determined the peculiarities of her axiology and poetics.

Disappearance is an inherent quality of the ‘trace’. A trace, moving within the ambiguous space between absence and presence, refers to some other event connected with it. In this essay, I apply my hybrid model of the trace, derived from the philosophies of Jacques Derrida, Charles Sanders Peirce, and Tim Ingold, in an analysis of the works of Ghanaian artist, Ibrahim Mahama. Mahama’s art responds to traces of failure and disappearance in the urban landscapes of Ghana. Working with materials and spaces in decay, Mahama maps residues of the past embedded in the material, tracing within its narratives of trade, migration, labour, capital, and commodity exploitation. By engaging communities around him in collaborative processes that are often large of scale and presented in public spaces, Mahama recollects memories of labour and exposes extreme histories that inform the present. [ABSTRACT FROM AUTHOR]

This paper is devoted to some selected topics of the theory of special orthogonal group SO(3). First, we discuss the trace of orthogonal matrices and its relation to the characteristic polynomial; on this basis, the partition of SO(3) formed by conjugation classes is described by trace mapping. Second, we show that every special orthogonal matrix can be expressed as the product of three elementary special orthogonal matrices. Explicit formulas for the decomposition as needed for applications in differential geometry and physics as symmetry transformations are given. [ABSTRACT FROM AUTHOR]

Can conventional rituals be meaningful? When and how can conventionality be part of processes of meaning-making rather than a mere obstacle that the cultural analyst must overcome? The article traces the meanings of minor rituals that populate the world of modern industrial societies and seem to have universal appeal. The article applies a Blochian regressive method to ethnological history in order to re-create the gradual process in which conventions appear, are disseminated, popularized, turned into group icons, and ritualized, and only then—and only sometimes—acquire discursive meanings that are often contested. This sequential model reveals the power of conventionality—the lack of contemplation about social conventions—in the processes of popularizing, ritualizing, and iconizing conventional acts. In the terms of Alexander's meaning-centered performance theory, this conventionality exemplifies a "perfect" or "effortless" fusion of performers and audience. The article thus argues that the meanings of conventional rituals—and perhaps also of conventional performances of more "sacred" rituals—often lie not in symbolic significance or semiotic thickness, but in deep conventionality : meaningfulness encoded in the convention itself. [ABSTRACT FROM AUTHOR]

The author describes how sociological and philosophical discussions of agency tend to center questions of how or why people are agentic rather than who or what is agentic. In contrast, the author poses questions about the agency of things, the agency of non-humans, and the agency of dead humans, using three examples of historical traces—Washington's refusal of a third term, Jenner's development of the smallpox vaccines, and Smith's publication of The Wealth of Nations —as historical examples to examine how non-humans and non-living-humans leave traces that can experienced as agentic. The author then analyzes six theories of agency that might provide explanations for these actions (actants, affordances, switchmen, residue, repression, and ghosts) before turning to his earlier work on the concept of "external authorities." [ABSTRACT FROM AUTHOR]

Background "Trace" results on Xpert MTB/RIF Ultra ("Ultra"; Cepheid) —a molecular diagnostic test for tuberculosis (TB)—are often interpreted as an indication for TB treatment, but may also represent detection of nonviable bacilli or analytical error. In community-screening settings where individual TB risk is low, there is limited guidance on how to interpret Ultra-trace results. Methods We conducted systematic Ultra TB screening of adults and adolescents (≥15 years) in Kampala, Uganda, through door-to-door and event-based sputum collection. We enrolled individuals with trace-positive sputum for detailed clinical, radiographic, and microbiological (including 2 sputum cultures, repeat Ultra, and for people with HIV, urine lipoarabinomannan) evaluation, and compared those findings with similar evaluations in controls with Ultra-negative and Ultra-positive (non-trace) sputum. Results Of 21 957 people screened with Ultra, 211 (1.0%) tested positive, including 96 (46% of positives) with trace results. Of 92 people enrolled with trace-positive sputum; 12% (11/92) were HIV-positive and 14% (13/92) had prior TB. The prevalence of TB among participants with trace-positive sputum results was 14% (13/92) by culture, 24% (22/92) using broader microbiological criteria, and 26% (24/92) after accounting for clinical diagnosis. The prevalence of cough and of abnormal chest computed tomography (CT) findings were 32% and 26%, respectively, if Ultra-negative; 34% and 54% if trace-positive/non–microbiologically confirmed; 72% and 95% if trace-positive/microbiologically confirmed; and 71% and 93% if Ultra-positive (more than trace). Conclusions Most individuals with trace-positive sputum in Ugandan communities did not have microbiologically confirmed TB but had more symptoms and chest CT abnormalities than people with Ultra-negative sputum. [ABSTRACT FROM AUTHOR]

We introduce and study a notion of module nuclear dimension for a C * -algebra A which is a C * -module over another C * -algebra 프 with compatible actions. We show that the module nuclear dimension of A is zero if A is 프 -NF. The converse is shown to hold when 프 is a C ⁢ (X) -algebra with simple fibers, with X compact and totally disconnected. We also introduce a notion of module decomposition rank, and show that when 프 is unital and simple, if the module decomposition rank of A is finite then A is 프 -QD. We study the set 풯 프 ⁢ (A) of 프 -valued module traces on A and relate the Cuntz semigroup of A with lower semicontinuous affine functions on the set 풯 프 ⁢ (A) . Along the way, we also prove a module Choi–Effros lifting theorem. We give estimates of the module nuclear dimension for a class of examples. [ABSTRACT FROM AUTHOR]

In this paper, we gave some generalized Young type inequalities due to Zuo and Li [J. Math. Inequal., 16 (2022), 1169-1178], and we also presented a new Young type inequality. As applications, we obtained some operator inequalities and matrix versions inequalities including the Hilbert-Schmidt norm and trace. [ABSTRACT FROM AUTHOR]

For any criminal prosecution officer, the crime scene investigation is one of the most important criminal prosecution actions and in most cases, it is also the starting point of investigations. Here, the traces left by the offender can be discovered, they can be visible or less visible, left due to negligence, haste, fear or on purpose. The traces, waiting to be discovered, form a significant part of the object of the forensic investigation. Being created in the environment through the actions of those involved in the commission of the offense, the traces contain a lot of information, including individual features of the perpetrator, and in turn are waiting to be discovered for the identification of the last. A hasty decision, a wrong step is able to compromise the deciphering of the crime scene and consequently the identification of the perpetrator. There is no such thing as a perfect crime, and in this initial work, the experience and knowledge of the criminal prosecution officer are essential to help him search, have a broad view and best understand the information he has already obtained. Professional experience is a condition of activation of the imagination, which will help him restoring the event of the offense in the form of its forensic characteristic. [ABSTRACT FROM AUTHOR]

Modern data centers provide the foundational infrastructure of cloud computing. Workload generation, which involves simulating or constructing tasks and transactions to replicate the actual resource usage patterns of real-world systems or applications, plays essential role for efficient resource management in these centers. Data center traces, rich in information about workload execution and resource utilization, are thus ideal data for workload generation. Traditional traces provide detailed temporal resource usage data to enable fine-grained workload generation. However, modern data centers tend to favor tracing statistical metrics to reduce overhead. Therefore the accurate reconstruction of temporal resource consumption without detailed, temporized trace information become a major challenge for trace-based workload generation. To address this challenge, we propose STWGEN, a novel method that leverages statistical trace data for workload generation. STWGEN is specifically designed to generate the batch task workloads based on Alibaba trace. STWGEN contains two key components: a suite of C program-based flexible workload building blocks and a heuristic strategy to assemble building blocks for workload generation. Both components are carefully designed to reproduce synthetic batch tasks that closely replicate the observed resource usage patterns in a representative data center. Experimental results demonstrate that STWGEN outperforms state-of-the-art workload generation methods as it emulates workload-level and machine-level resource usage in much higher accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we gave some generalized Young type inequalities due to Zuo and Li [J. Math. Inequal., 16 (2022), 1169-1178], and we also presented a new Young type inequality. As applications, we obtained some operator inequalities and matrix versions inequalities including the Hilbert-Schmidt norm and trace.

I will tackle serial appropriations of Shakespeare’s Macbeth in The Wire (David Simon, 2002–2008) and Breaking Bad (Vince Gilligan, 2008–2013). Both complex TV series recast Macbeth in the context of narcocapitalism. Rather than constituting an alternative to mainstream capitalism, narco-capitalism maintains the American and global socioeconomic orders as depicted in both series. Paying attention to what will be defined as Shakespeare’s archive, it will be shown that traces from Macbeth are reactivated in The Wire and Breaking Bad. Shakespeare’s archive is formed by traces of Shakespeare’s dramatic and narrative sources, quartos, folios, later editions and adaptations. This corpus displays verbal and non-verbal features of Shakespeare’s oeuvre. Taken together, traces and reenactments of Shakespeare highlight the multifarious and competing ways in which Shakespearean appropriations sail through the depth and length of complex TV. To illustrate this, I will use archive theory, transmedia theory and narcocapitalism as lenses of analysis. This framework helps explain archival strategies employed for Shakespearean appropriation within the social context of both series. The results reveal that Shakespeare’s archive in both works leads to an ambivalent ethical assessment of the potentialities of narco-capitalism.

The Sierpinski gasket K has three line segments constituting a regular triangle as its border. This paper studies what will happen if one of them, which is called the bottom line and is denoted by I, is removed from K. At a glance, “the Sierpinski gasket minus the bottom line” K \ I has a structure of a tree of Sierpinski gaskets. This observation leads us to the results showing that the boundary of K \ I is not the line segment I but a Cantor set from viewpoints of geometry and analysis. As a by-product, we have an explicit expression of the jump kernel of the trace of the Brownian motion of K on the bottom line I. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of traces for Sobolev spaces on the hyperbolic filling X of a compact metric space Z equipped with a doubling measure. Given a suitable metric on X, we can regard Z as the boundary of X. After equipping X with a weighted measure μ ρ via the measure on Z and the Euclidean arc length, we give characterizations for the existence of traces for first-order Sobolev spaces. [ABSTRACT FROM AUTHOR]