Extension Property Research Articles

Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders

Entanglement constitutes one of the key concepts in quantum mechanics and serves as an indispensable tool in the understanding of quantum many-body systems. In this work, we perform extensive numerical investigations of extensive entanglement properties of coupled quantum spin chains. This setup has proven useful for e.g. extending the Lieb–Schultz–Mattis theorem to open systems, and contrasts the majority of previous research where the entanglement cut has one lower dimension than the system. We focus on the cases where the entanglement Hamiltonian is either gapless or exhibits spontaneous symmetry breaking behavior. We further employ conformal field theoretical formulae to identify the universal behavior in the former case. The results in our work can serve as a paradigmatic starting point for more systematic exploration of the largely uncharted physics of extensive entanglement, both analytical and numerical.

Impacts of Gorkha Earthquakes: A Comprehensive Study

Nepal is highly vulnerable to seismic activity. This review seeks to explore the impact of earthquakes on human populations in terms of casualties and injuries, as well as to pinpoint the risk factors associated with these outcomes. An earthquake measuring 7.8 on the Richter scale struck near Gorkha, Nepal, on April 25, 2015, resulting in the loss of nearly nine thousand lives, extensive property damage, and the destruction of numerous historical and cultural landmarks. Data sourced from the UNDRR, Ministry of Home Affairs, and the United States Geological Survey were analyzed using the ArcGIS software tool. The study offers a comprehensive examination of earthquake-prone regions at regional, national, and global levels. By analyzing recent significant earthquakes along with their associated losses and damages, it underscores the importance of precautionary measures and risk analysis in reducing vulnerability and enhancing preparedness among researchers and stakeholders.

Pseudo-Eutectic of Isodimorphism to Design Biaxially-Oriented Bio-Based PA56/512 with High Strength, Toughness and Barrier Performances.

The biaxially-oriented PA56/512 has excellent mechanical strength, extensibility and water-oxygen barrier properties and has broad application prospects in green packaging, lithium battery diaphragm and medical equipment materials. The correlation between the aggregation structure evolution and macroscopic comprehensive properties of copolymer PA56/512 under biaxial stretching has been demonstrated in this work. The structure of the random copolymerization sequence was characterized by 13C Nuclear magnetic resonance (NMR). The typical isodimorphism behavior of the co-crystallization system of PA56/512 and its BOPA-56/512 films was revealed by differential scanning calorimetry (DSC) and X-ray diffraction (XRD) tests. And the aggregation structure, including the hydrogen bond arrangement, crystal structure and crystal morphology of PA56/512 before and after biaxial stretching, was investigated by XRD, Fourier-transform infrared spectroscopy (FTIR) and polarized optical microscopy (POM) tests. Furthermore, the effect of the biaxially-oriented stretching process on the mechanical properties of PA56/512 has been demonstrated. In addition, a deep insight into the influence of the structure on the crystallization process and physical-mechanical performance has been presented. The lowest melting point at a 512 content of 60 mol% is regarded as a "eutectic" point of the isodimorphism system. Due to the high disorder of the structural units in the polymer chain, the transition degree of the folded chain (gauche conformation) is relatively lowest when it is straightened to form an extended chain (trans conformation) during biaxially-oriented stretching, and part of the folded chain can be retained. This explains why biaxially stretched PA56/512 has high strength, outstanding toughness and excellent barrier properties at the pseudo-eutectic point. In this study, using the unique multi-scale aggregation structure characteristics of a heterohomodymite polyamide at the pseudo-eutectic point, combined with the new material design scheme and the idea of biaxial-stretching processing, a new idea for customized design of high-performance multifunctional polyamide synthetic materials is provided.

Markov and Division Inequalities on Algebraic Sets

A compact set E⊂CN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E\\subset \\mathbb {C}^N$$\\end{document} satisfies the Markov inequality if the supremum norm on E of the gradient of a polynomial p can be estimated from above by the norm of p multiplied by a constant polynomially depending on the degree of p. This inequality is strictly related to the Bernstein approximation theorem, Schur-type estimates and the extension property of smooth functions. Additionally, the Markov inequality can be applied to the construction of polynomial grids (norming sets or admissible meshes) useful in numerical analysis. We expect such an inequality with similar consequences not only on polynomially determining compacts but also on some nowhere dense sets. The primary goal of the paper is to extend the above definition of Markov inequality to the case of compact subsets of algebraic varieties in CN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {C}^N$$\\end{document}. Moreover, we characterize compact sets satisfying such a Markov inequality on algebraic hypersurfaces as well as on certain varieties defined by several algebraic equations. We also prove a division inequality (a Schur-type inequality) on these sets. This opens up the possibility of establishing polynomial grids on algebraic sets. We also provide examples that complete and ilustrate the results.

Fishing gear with enhanced drapability and biodegradability: Artificial, eco-friendly fibers inspired by the mussel byssus

Abandoned, lost, and discarded fishing gear (ALDFG) poses a global challenge for marine ecosystems because it results in the destruction of algal forests, the largest oceanic carbon dioxide sinks. Biodegradable polybutylene succinate (PBS), which has a tensile strength similar to that of nylon, has been suggested as a potential fishing-gear material. However, its slow degradation in the marine environment and limited drapability need to be addressed before it can be used in environmentally friendly fishing gear. Inspired by the mussel byssus, a thread-like holdfast known for its stiff yet extensible mechanical properties, we developed fishing gear using a mussel-byssus-mimetic fiber (artificial byssus fiber, ABf) structure. The ABf was composed of poly(butylene adipate-co-butylene terephthalate) (PBAT) fibers with favorable draping characteristics coated with mechanically resilient and PBS, which demonstrated sufficient toughness and draping properties for use in fishing gear. AB shows promise as a material for fishing-gear capable of mitigating issues related to ALDFG, especially given its marine degradability by microbial strains that degrade PBS and PBAT. Furthermore, it could serve as a substrate for ocean afforestation, given the improved settlement and growth of seaweed spores (Pyropia yezoensis) on AB. Overall, AB-based fishing gear is expected to enhance macroalgal forest conservation and expansion and facilitate marine carbon capture through marine afforestation.

Geophysical Modeling of the Bjerkreim-Lobe, Southern Norway

Summary The Bjerkreim-Sokndal intrusion in southern Norway has been studied for decades due to the presence of magnetic remanence creating anomalies 12000 nT below background as measured by airborne magnetic surveys. The strong magnetic remanence also makes the Bjerkreim-Sokndal intrusion a good Earth analogue for remote studies of planets that have prominent magnetic signatures, such as Martian geologic environments. Although numerous geophysical surveys and samples have been collected in the area, there are limited 3D geological interpretations of the subsurface. Here, we used existing geophysical data to conduct forward and inversion modeling of the Bjerkreim lobe to investigate the subsurface geometry of the Bjerkreim-Sokndal intrusion. An extensive petrophysical property compilation was used as input data for the models, in combination with airborne magnetics and digital elevation models. This petrophysical compilation was initially analyzed using Principal Component Analysis to understand which variables would have the greatest impact on the models. Forward and inversion modeling show that crosscutting jotunite bodies, and small anorthosite blocks within the Bjerkreim lobe have a limited depth extent of 1 km. Massive and foliated anorthosites to the west of the Bjerkreim lobe extend to depths greater than 4 km indicating that the Bjerkreim-Sokndal intruded into these anorthosites. Complications in magnetic field fitting during the forward modeling of megacyclic units with strong magnetic remanence and the results from a new ground magnetic survey support the need to revisit mapped contacts of the cyclical units.

A new hybrid odd exponential-Φ family: Properties and applications

The paper introduces the hybrid odd exponential-Φ (HOE-Φ) family, a novel framework for generating a continuous distribution characterized by an additional parameter. The extensive statistical properties of this family are derived and explored in detail. Parameter estimation is performed using the maximum likelihood estimation technique. The efficacy and versatility of the proposed model are demonstrated through a comparative analysis involving two distinct real-world datasets.

Semiconic idempotent logic I: Structure and local deduction theorems

Semiconic idempotent logic is a common generalization of intuitionistic logic, relevance logic with mingle, and semilinear idempotent logic. It is an algebraizable logic and it admits a cut-free hypersequent calculus. We give a structural decomposition of its characteristic algebraic semantics, conic idempotent residuated lattices, showing that each of these is an ordinal sum of simpler partially ordered structures. This ordinal sum is indexed by a totally ordered residuated lattice, which serves as its skeleton and is both a subalgebra and nuclear image. We equationally characterize the totally ordered residuated lattices appearing as such skeletons. Further, we describe both congruence and subalgebra generation in conic idempotent residuated lattices, proving that every variety generated by these enjoys the congruence extension property. In particular, this holds for semilinear idempotent residuated lattices. Based on this analysis, we obtain a local deduction theorem for semiconic idempotent logic, which also specializes to semilinear idempotent logic.

A General Theoretical Framework for Learning Smallest Interpretable Models

We develop a general algorithmic framework that allows us to obtain fixed-parameter tractability for computing smallest symbolic models that represent given data. Our framework applies to all ML model types that admit a certain extension property. By showing this extension property for decision trees, decision sets, decision lists, and binary decision diagrams, we obtain that minimizing these fundamental model types is fixed-parameter tractable. Our framework even applies to ensembles, which combine individual models by majority decision.

Sobolev, BV and perimeter extensions in metric measure spaces

We study extensions of sets and functions in general metric measure spaces. We show that an open set has the strong BV-extension property if and only if it has the strong extension property for sets of finite perimeter. We also prove several implications between the strong BV-extension property and extendability of two different non-equivalent versions of Sobolev \(W^{1,1}\)-spaces and show via examples that the remaining implications fail.

Heat kernel for reflected diffusion and extension property on uniform domains

Heat kernel for reflected diffusion and extension property on uniform domains

Li3V2(PO4)3 Cathode Material: Synthesis Method, High Lithium Diffusion Coefficient and Magnetic Inhomogeneity.

Li3V2(PO4)3 cathodes for Li-ion batteries (LIBs) were synthesized using a hydrothermal method with the subsequent annealing in an argon atmosphere to achieve optimal properties. The X-ray diffraction analysis confirmed the material's single-phase nature, while the scanning electron microscopy revealed a granular structure, indicating a uniform particle size distribution, beneficial for electrochemical performance. Magnetometry and electron spin resonance studies were conducted to investigate the magnetic properties, confirming the presence of the relatively low concentration and highly uniform distribution of tetravalent vanadium ions (V4+), which indicated low lithium deficiency values in the original structure and a high degree of magnetic homogeneity in the sample, an essential factor for consistent electrochemical behavior. For this pure phase Li3V2(PO4)3 sample, devoid of any impurities such as carbon or salts, extensive electrochemical property testing was performed. These tests resulted in the experimental discovery of a remarkably high lithium diffusion coefficient D = 1.07 × 10-10 cm2/s, indicating excellent ionic conductivity, and demonstrated impressive stability of the material with sustained performance over 1000 charge-discharge cycles. Additionally, relithiated Li3V2(PO4)3 (after multiple electrochemical cycling) samples were investigated using scanning electron microscopy, magnetometry and electron spin resonance methods to determine the extent of degradation. The combination of high lithium diffusion coefficients, a low degradation rate and remarkable cycling stability positions this Li3V2(PO4)3 material as a promising candidate for advanced energy storage applications.

Determination of progressive damage modelling parameters and calibration studies of 8-harness satin weave S-2 glass fibre reinforced composites

The aim of this article is to present a progressive damage modelling study of 8-harness satin weave S-2 glass fibre-reinforced SC15 epoxy matrix composites. Extensive mechanical properties of the composite were investigated throughout the study. The material was subjected to low-velocity impact (LVI) loading for investigating progressive damage. MAT162 material model in Ls-Dyna commercial finite element software was chosen for modelling damage that occurred in composite structure at the end of LVI test. MAT162 needs different material properties including elastic and strength properties with additional damage parameters. Different standard and non-standard tests were conducted to obtain these properties. Additionally, numerical simulation studies were run to calibrate these material properties. Finally, a set of calibrated material properties of 8HS-S2G/SC15 composite were obtained.

Challenges and Opportunities in Addressing Armed Banditry in Nigeria’s Northwest: Insights from the Field

In recent years, the escalation of armed banditry in the northwestern region of Nigeria has reached alarming proportions, leading to significant loss of life and extensive property damage amounting to billions of Naira. While numerous studies have delved into the causes and repercussions of this crisis, there remains a notable gap in addressing the challenges and opportunities inherent in combating this menace. This paper diverges from existing research by conducting an analytical examination of the obstacles and prospects involved in mitigating the issue. Drawing upon fieldwork conducted in Katsina and Zamfara states, it sheds light on grassroots perspectives, emphasizing the crucial role of local communities in the broader efforts to counter armed banditry in northwestern Nigeria. The study underscores the necessity of integrating affected populations into comprehensive strategies aimed at curbing the menace. Ultimately, it advocates for urgent and coordinated action by both national and state governments to address the underlying causes of the crisis.

Significance of radiation on the Brinkman-type nanofluid with variable surface velocity embedding with porous matrix

The current flow phenomena based on the flow of water-based nanofluid corresponding to the variable surface velocity. Further, the electrically conducting fluid embedding with porous matrix with an inclusion of thermal radiation enriches the study as well. Because of the varied industrial applications for the use of nanoparticle concentration with radiating heat that is used in cooling process has significant role for the enhancement of heat transport properties. Besides to it in several other applications like engineering, biomedical, and nuclear science the contribution of nanoparticle shows its extensive properties. The main goal of the proposed investigation is to study the influence of thermal radiation on the Brinkman-type nanofluid in the presence of porous matrix. Further, the behavior of variable surface velocity enriches the study. The proposed designed time dependent model associated with various physical restrictions is taken care of analytically using Laplace Transformation Technique and their behavior is deliberated through graphs. However, the validation as well as convergence criteria of the present methodology correlate with the earlier investigation.

Introducing UCST onto Chitosan for a Simple and Effective Single-Phase Extraction.

Upper critical solution temperature (UCST) polymers undergo their own collapsed structures to show thermoresponsive functions favoring controlled release systems, cell adhesion, including separation process, etc. Although the copolymerization of UCST monomers with other vinyl monomers containing a pendant group is a good way to introduce additional functions, uncertain UCST performance as well as extensive bio-related properties are always the points to be considered. To accomplish this, the present work proposes the application of polysaccharides, i.e., chitosan (CS), as the biopolymer backbone to conjugate with functional molecules and UCST polymers. The use of chain transfer agents, e.g., mercaptoacetic acid, in radical polymerization with UCST poly(methacrylamide) (PMAAm) via the CS/NHS (N-hydroxysuccinimide) complex allows the simple water-based modification. The further conjugation of mouse anti-LipL32 IgG monoclonal antibody (anti-LipL32 mAb) onto CS-PMAAm (CS-PMAAm-Ab) enables a selective binding of recombinant LipL32 (rLipL32) antigen (Ag) in the solution. The CS-PMAAm obtained not only shows the cloud point in the range of 10-30 °C but also the extraction of rLipL32 because of CS-PMAAm-Ab-Ag aggregation. The present work demonstrates how CS expresses UCST with additional antibody conjugated is feasible for a simple and effective Ag single-phase extraction.

Agricultural waste as a sustainable source for nanoparticle synthesis and their antimicrobial properties for food preservation

Traditional agriculture from cropping to harvesting is contributing to climate change by increasing global greenhouse emissions. Circular economy approaches and biorefinery technologies based on the reuse, recycling, and remanufacturing might result in the valorization of wastes that consequently would avoid environmental pollution. Nanoparticles synthesis using bio-waste such as stems, leaves, seeds, pulp, stubble, and bagasse is considered a green approach with low energy consumption, and low-cost production. Characteristics of raw materials influence the final application of nanoparticles in edible coatings, and films. Therefore, the preparation of nanoparticles based on cellulose, pectin, metal (titanium oxide, silver, zinc oxide), or silica are considered organic, inorganic, or hybrid nanocomposites, are resulted in several benefits including shelf-life extension and broad-spectrum antimicrobial properties by its capacity to encapsulate active compounds that greatly improve food preservation. For considering agro-waste-based nanoparticles in food, challenges in homogenization and synthesis, yield, and toxicity are mainly described. Therefore, this review examines the employment of agro-industrial waste for the development of sustainable nanoparticles and their synthesis methods (top-down and bottom-up). Moreover, it discusses their incorporation and role in active edible coatings and films by highlighting their bioactive properties, mechanisms of action, and applications in food group preservation.

Notes on smooth and singular volumetric growth

The material structure of bodies undergoing growth is considered. In the geometric framework of a general differential manifold modeling the physical space and a fiber bundle modeling spacetime, body points may be defined for any extensive property for which a smooth flux field exists, even if the property is not conserved. Singular flux fields are considered using the notion of a de Rham current. Writing a generalized balance law using the boundary of the current corresponding to a singular flux field, surface growth is unified with volumetric growth.

Phytochemical and pharmacological review of cynodon dactylon grass with its potential effects

Perennial herb Cynodon dactylon (L) Pers, family: Poeaceae, widespread throughout India. In several Indian languages, it is referred to by different names, including Durva in Marathi, Durba in Bengali, Dhro in Gujarati, Garichgaddi in Telugu, Arukampillu in Tamil, and Shataparva in Sanskrit. In traditional medical systems and ethnomedical practices, Cynodon dactylon plays a significant role. It is used in the form of powder, paste, or juice to treat a wide range of ailments due to its extensive therapeutic properties. Flavanoids, alkaloids, glycosides, terpenoides, triterpenoids, steroids, saponins, tannins, resins, phytosterols, reducing sugars, carbohydrates, proteins, volatile oils, and fixed oils were all found in Cynodon dactylon, according to the phytochemical examination. According to earlier research, Cynodon dactylon has properties that are protective, antimicrobial, antiparasitic, insecticidal, gastrointestinal, antioxidant, immunological, antiallergic, antiinflammatory, antipyretic, analgesic, anticancer, dermatological, diuretic, and immune system-related was found. In given review we studied some pharmacological aspects of Perennial herb Cynodon dactylon as well its versitile potential effect. The wide range of future aspects we can consider as best alternative medicine over chemical drugs.

After a Century of Revolution in the Status of Space and Time: Einstein’s Train Revisited

Written from a very untutored and limited viewpoint in terms of physics and mathematics, this essay ventures some thoughts that should therefore be regarded as only tentative. Especially as they address a long established idea that sits right at the heart of the scientific discipline of physics. This is the idea of naturally moving reference systems, a notion closely linked to the classical principles of both inertia and relativity. Such inertial reference systems played a key role in some thought experiments published over a century ago, by Albert Einstein. It is a critical reading of one of these original accounts that forms a springboard for some radical discussions, particularly in terms of assumptions about the physical nature of space. The remarkable revolution in such views that’s taken place since Einstein’s younger days is considered. A development more in accord with this sort of fundamentally modernised world-view suggests a re-appraisal and expanded inclusivity for the inertial reference system concept. In the old thought experiment account in question, Einstein famously used an imaginary device — a train struck by lightning — to illustrate his earlier reasoning for one of his most revolutionary and enduring concepts: the relativity of simultaneity. Over the century or more since he first put this basic rationale forward in 1905, it’s clear it has been largely received with widespread scientific approval. Yet in fact, it’s also apparent that Einstein’s argument actually depended solely on employing the logic of classical mechanics — albeit well beyond its established domain of application. And it’s very troubling that by showing such a clear preference for this old and very conventional but intuitively attractive approach, in effect he allowed it to directly contradict the predictive force of his own new and revolutionary postulates. In response to this concern, a sort of remedial analysis was undertaken. It accepted Einstein’s famous postulates and simply applied them directly to his train scenario — quite independently of the classical transformation he chose to employ instead. It is shown how this meticulous reanalysis led unambiguously to a very different inference about the question of simultaneity. The logical result of applying the postulates was very clear: the observed simultaneity of events is actually not relative to perspective. Rather, this temporal quality seems to be thoroughly conserved across different reference frames, in line with the idea of a universal passage of time. An idea which a majority of physicists probably now consider to be entirely obsolete. They would see the relativity of simultaneity as an integral and established part of the legacy of Einstein’s spectacularly successful theorising. Evaluating what to make of this strikingly disparate and seemingly anomalous outcome compared to Einstein’s, leads to discussions set in a more philosophical context. First, a brief overview portrays how metaphysical views on the status of space have radically evolved over the last century. Adopting a more present-day style of understanding, it is suggested how the old notion of naturally moving systems might need to be newly characterised. While inertial reference systems may continue to be conceived as spatially related frameworks of material bodies, all moving uniformly and in unison, this may not represent all that they really are. In addition, it may now be necessary to recognise the significance of a further content for inertial systems. They should be seen as including areas of discrete and equally co-moving spatial and physical field. Such spatial aspects of reference systems have previously been regarded only as matter-based, geometrical abstractions. They were regarded only as part of a spatial framework derived from the coordinates representing the extension properties of an independent background of immobile and empty space, through which the whole framework of matter is moving. However, from current perspectives on the nature of space, these additional contents could well comprise individuated and co-moving aspects of a highly dynamic and distinctly physical entity. Taken together across multiple reference frames, these co-moving spatial contents would constitute a flexing continuum of super-plastic and holistically extended dynamic fields — such as electric and magnetic fields. On this conjectural basis the propagation of light would indeed show a constant ‘vacuum’ speed when directly measured in ‘resting’ space, just as both Einstein and Maxwell required. But, if a particular reference perspective is artificially adopted as absolutely stationary, or likewise, singled out as the preferred and real viewpoint, then it is explained how its speed relative to light propagating elsewhere might then be considered as basically Galilean in nature, not unlike the situation with the passage of sound. Even so, the fact that the classical transformation procedure has so clearly been superseded by the more generally efficacious Lorentz transformations of the Special Theory of Relativity is certainly not denied. However, the veracity of their assumed basis in the physical length contraction of inertially moving matter and its associated physical time dilation is seriously questioned. In criticising some aspects of Einstein's earliest assumptions that underpinned his Special Relativity Theory, this essay promotes a view which suggests that some of this thinking would have benefitted from being more relativistic, not less