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Two polyhedral silver‐thiolate clusters, [S@Ag16(Tab)10(MeCN)8](PF6)14 (Ag16) and [Ag12(Tab)6(DMF)12](PF6)12 (Ag12), were synthesized by using electroneutral Tab species as protective ligands (Tab=4‐(trimethylammonio)benzenethiolate, DMF=N,N‐dimethylformamide, MeCN=acetonitrile). Ag16 has a decahedral shape composed of eight pentagon {Ag5} units and two square {Ag4} units. The structure of Ag12 is a cuboctahedron, a classical Archimedean structure composed of six triangular faces and eight square faces. The former configuration is discovered in silver‐thiolate cluster for the first time, possibly benefited from the more flexible coordination between the Tab ligand and Ag+ facilitated by the electropositive −N(CH3)3+ substituent group. Third‐order nonlinear optical studies show that both clusters in DMF exhibit reverse saturate absorption response under the irradiation of 532 nm laser. [ABSTRACT FROM AUTHOR]

It is known that the flip distance between two triangulations of a convex polygon is related to the smallest number of tetrahedra in the triangulation of some polyhedron. The latter was used to compute the diameter of the flip graph of convex polygons with a large number of vertices. However, it is yet unknown whether the flip distance and this smallest number of tetrahedra are always the same or even close. In this work, we find examples to show that the ratio between these two numbers can be arbitrarily close to 32 $\frac{3}{2}$. We also propose two conjectures in the end, one about this ratio, and the other may have some implications on when two triangulations can achieve maximal distance. [ABSTRACT FROM AUTHOR]

Innovation in comminution is expected to continue unabated to address the inefficiencies that are inherent in comminution circuits. The rotary offset crusher (ROC) is a new comminution device with a promising performance potential in terms of throughput due to the enhanced speed of transportation induced by the centrifugal force of the discs. However, the processes driving the comminution of particles trapped in the conical space between the two discs of the crusher are not fully understood. To gain a better insight into the comminution process in this device, discrete element modeling (DEM) simulations were conducted to study the breakage of a single particle for the crusher operated under two different dynamic conditions, i.e., (1) a stationary top disc and (2) both discs rotating at the same speed. For both scenarios, the speed of the discs was varied between 550 and 2350 rpm. Experimental testwork was also conducted with the laboratory prototype to generate the data that were used to calibrate the breakage parameters of the Ab × t10 breakage model. Simulations were performed using polyhedral UG2 ore particles that were generated with the in-built particle generator in the DEM simulator. The simulated ROC, which is operated with both discs rotating, outperformed the ROC with a stationary top disc in terms of the specific input energy and throughput. The crusher with a stationary top disc is characterized by high shear forces (suggesting a higher wear rate), specific input energies greater than 1 kWh/t, and low throughputs (<50 kg/h). The ROC operated with a stationary disc is not recommended for hard rock applications due to expected excessive wear of crushing surfaces and higher energy consumption. The freewheeling discs are recommended, but there is scope to optimize the crusher performance in terms of the power draw, size reduction, and throughput by manipulating the difference between the speeds of the discs. There is also scope to optimize the crusher performance when it is simulated with many particles. Once the full performance potential of the ROC is established, it will then be important to benchmark it against the existing crushers in the minerals industry as well as other industries where crushers are used. [ABSTRACT FROM AUTHOR]

In our previous paper, it is proved that for any positive flow-spine P of a closed, oriented 3-manifold M, there exists a unique contact structure supported by P up to isotopy. In particular, this defines a map from the set of isotopy classes of positive flow-spines of M to the set of isotopy classes of contact structures on M. In this paper, we show that this map is surjective. As a corollary, we show that any flow-spine can be deformed to a positive flow-spine by applying first and second regular moves successively. [ABSTRACT FROM AUTHOR]

Polyhedrons, spheroids and bolas (PSBs) have been found in lithic series spanning two million years, but their purpose remains largely unknown. In this study, we propose a functional analysis of PSBs from nine assemblages from France and North Africa, ranging from 1.78 to 0.169 Ma. By combining use-wear, ergonomic and metric analyses with sequential experiments, we explore the meaning and diversity of these objects. Our experiments revealed two key findings: 1) the manufacture process creates intense traces on removal scars used as striking platforms, and 2) the existence of a paradox between the complexity of the manufacture process and their efficiency equal to that of cobbles. This can question the purpose of manufacturing a PSB instead of using a pebble, and may suggest an opportunistic recycling of PSB “preforms” (e.g. pebble tools, cores) in some cases. Our results also suggest that PSBs encompass a wide diversity of pieces with a cubical to rounded final shape. These objects may have been primarily used in heavy-duty tasks, some being possibly involved in different types of percussive activities (active or passive). Interestingly, our analyses suggest that there are similarities between PSBs respectively in South-western Europe and North Africa. By studying PSBs, we can gain insights not only into hominin behaviours, but also into regional traditions and the diffusion of techno-cultural practices during the Palaeolithic. [ABSTRACT FROM AUTHOR]

Three hundred years ago, Prince Rupert of Rhine showed that a unit cube has the property that one copy of it can be passed through a suitable hole in another copy. Under this situation, we say that a unit cube has the Rupert property. In the past years, there are many research studying about the Rupert property of many solids in R 3 . For higher dimensions, the n-dimensional cube and the regular n-simplex were studied to have the Rupert property. In this work, we focus on the Rupert property of some polyhedrons in n dimensions. In particular, we show that some particular n-dimensional simplices, generalized n-dimensional octahedrons and some related solids in R n have the Rupert property using arbitrarily small rotations and translations. [ABSTRACT FROM AUTHOR]

We prove a comparison theorem for certain types of polyhedra in a 3-manifold with its scalar curvature bounded below by -6. The result confirms in some cases the Gromov dihedral rigidity conjecture in hyperbolic 3-space. [ABSTRACT FROM AUTHOR]

The article intends to present, in a primarily descriptive way, the fundamental features of the rich and varied itinerary - although bumpy and not always linear - of the reception of the conciliar decree on ecumenism Unitatis redintegratio, in the various articulations of catholicity. The post-conciliar time is divided into four stages: the first post-Council period and the expectation of an ecumenical spring; John Paul II and the season of popular ecumenism; ecumenism in the clash of civilizations storm; Pope Francis and the ecumenism of the polyhedron and of walking together. What is implied in this article is that, more than one hundred years after the start of the ecumenical movement, for today's Christians, who are immersed in the culture of post-modernity, dialogue between the churches should not be one option among many, to be pursued or not depending on the seasons, but the common form of being Christian today. [ABSTRACT FROM AUTHOR]

A closed quasigeodesic on a convex polyhedron is a closed curve that is locally straight outside of the vertices, where it forms an angle at most π on both sides. While the existence of a simple closed quasigeodesic on a convex polyhedron has been proved by Pogorelov in 1949, finding a polynomial-time algorithm to compute such a simple closed quasigeodesic has been repeatedly posed as an open problem. Our first contribution is to propose an extended definition of quasigeodesics in the intrinsic setting of (not necessarily convex) polyhedral spheres, and to prove the existence of a weakly simple closed quasigeodesic in such a setting. Our proof does not proceed via an approximation by smooth surfaces, but relies on an adaptation of the disk flow of Hass and Scott to the context of polyhedral surfaces. Our second result is to leverage this existence theorem to provide a finite algorithm to compute a weakly simple closed quasigeodesic on a polyhedral sphere. On a convex polyhedron, our algorithm computes a simple closed quasigeodesic, solving an open problem of Demaine, Hersterberg, and Ku. [ABSTRACT FROM AUTHOR]

We show that the multistage stochastic linear problem (MSLP) with an arbitrary cost distribution is equivalent to an MSLP on a finite scenario tree. We establish this exact quantization result by analyzing the polyhedral structure of MSLPs. In particular, we show that the expected cost-to-go functions are polyhedral and affine on the cells of a chamber complex, which is independent of the cost distribution. This leads to new complexity results, showing that MSLP becomes polynomial when certain parameters are fixed. [ABSTRACT FROM AUTHOR]

This paper provides a complete determination of which of the alternating groups A n and the symmetric groups S n occur as the automorphism group of some regular or chiral map on an orientable surface, and which of them occur as the automorphism group of a regular map on a non-orientable surface. The situation for some given types (m , k) is also considered, where k is the valency and m is the face-size, with special focus on types with m = 3 , and more particularly with (m , k) = (3 , 7) or (3 , 8) , or their duals. Some observations are made also about what happens for regular and orientably-regular maps with given valency, and for regular and chiral polyhedra. Much but certainly not all of what is presented follows from theorems in previous papers by the author and others, and this one brings them and some new observations together into a single reference. [ABSTRACT FROM AUTHOR]

Grasserie is a major infectious disease of silkworms caused by the Bombyx mori nuclear polyhedrosis virus. The virus belongs to the family Baculoviridae and is composed of a polyhedron with a single molecule of circular supercoiled double-stranded deoxyribose nucleic acid. The disease causes massive mortality (more than 60% of the total crop loss caused by different diseases), causing significant great crop loss to the sericulturists by reducing the cocoon crop and silk produce. There has been no effective solution for preventing and treating the disease. In the present review, the authors explore the subject in detail and inspire the researchers to search for molecular mechanisms of gene action and promote disease-resistant silkworm breeding. [ABSTRACT FROM AUTHOR]

A study is performed of the self-diffusion of tritium and fluorine atoms, and the change in the structure of molten FLiBe upon raising the temperature of the system from 873 to 1073 K. The interaction between neutrons and both lithium and beryllium in molten-salt reactors (MSR) using FLiBe as a fuel salt results in the formation of large amounts of tritium. Tritium, which easily penetrates metallic structural materials at high temperatures, is a radionuclide hazard. Predictive models for the behavior of tritium in a molten fluoride salt must therefore be developed to solve the problem of MSR safety. The emergence of tritium in the system increases the average energy of interatomic bonds upon raising the temperature and concentration of tritium in the system. A rise in temperature is also accompanied by fluorine atoms creating a closer short-range order in the environment of tritium atoms. This is expressed in the formation of a high first peak of radial distribution function , an increase in the number of probable geometric neighbors, which is shown by Voronoi polyhedra, and fluorine atoms giving priority to fourth-order rotational symmetry in the environment of tritium atoms. [ABSTRACT FROM AUTHOR]

A self-affine tile is a compact set G ⊂ R d that admits a partition (tiling) by parallel shifts of the set M - 1 G , where M is an expanding matrix. We find all self-affine tiles which are polyhedral sets, i.e., unions of finitely many convex polyhedra. It is shown that there exists an infinite family of such polyhedral sets, not affinely equivalent to each other. A special attention is paid to integral self-affine tiles with standard digit sets, when the matrix M and the translation vectors are integer. Applications to the approximation theory and to the functional analysis are discussed. [ABSTRACT FROM AUTHOR]

We prove that, given a polyhedron P in R 3 , every point in R 3 that does not see any vertex of P must see eight or more edges of P , and this bound is tight. More generally, this remains true if P is any finite arrangement of internally disjoint polygons in R 3 . We also prove that every point in R 3 can see six or more edges of P (possibly only the endpoints of some these edges) and every point in the interior of P can see a positive portion of at least six edges of P . These bounds are also tight. [ABSTRACT FROM AUTHOR]

A flow-spine of a 3-manifold is a spine admitting a flow that is transverse to the spine, where the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. We say that a contact structure on a closed, connected, oriented 3-manifold is supported by a flow-spine if it has a contact form whose Reeb flow is a flow of the flow-spine. It is known by Thurston and Winkelnkemper that any open book decomposition of a closed oriented 3-manifold supports a contact structure. In this paper, we introduce a notion of positivity for flow-spines and prove that any positive flow-spine of a closed, connected, oriented 3-manifold supports a contact structure uniquely up to isotopy. The positivity condition is critical to the existence of the unique, supported contact structure, which is also proved in the paper. [ABSTRACT FROM AUTHOR]

Innovation in comminution is expected to continue unabated to address the inefficiencies that are inherent in comminution circuits. The rotary offset crusher (ROC) is a new comminution device with a promising performance potential in terms of throughput due to the enhanced speed of transportation induced by the centrifugal force of the discs. However, the processes driving the comminution of particles trapped in the conical space between the two discs of the crusher are not fully understood. To gain a better insight into the comminution process in this device, discrete element modeling (DEM) simulations were conducted to study the breakage of a single particle for the crusher operated under two different dynamic conditions, i.e., (1) a stationary top disc and (2) both discs rotating at the same speed. For both scenarios, the speed of the discs was varied between 550 and 2350 rpm. Experimental testwork was also conducted with the laboratory prototype to generate the data that were used to calibrate the breakage parameters of the Ab × t10 breakage model. Simulations were performed using polyhedral UG2 ore particles that were generated with the in-built particle generator in the DEM simulator. The simulated ROC, which is operated with both discs rotating, outperformed the ROC with a stationary top disc in terms of the specific input energy and throughput. The crusher with a stationary top disc is characterized by high shear forces (suggesting a higher wear rate), specific input energies greater than 1 kWh/t, and low throughputs (

The difficulty of learning to build polyhedron for middle students makes experts lecturers collaboratively create learning trajectories through the Lesson Study for Learning Community (LSLC). This study aims to produce a learning trajectory that can assist students in learning polyhedron using collaborative learning through LSLC. The research method used was design research with the first stage, preparing for experiment, experimental design, and retrospective analysis. This learning approach uses collaborative LSLC is used in the process of making teaching materials and along with research methods. This study involved 47 lecturers and 24 mathematics education students. Data collection was carried out through observing student activities, recording video events in class, collecting student work results, and student test results. The collected data were then analyzed retrospectively with the results showing that collaborative and LSLC used in the acquired learning paths can help students in learning flat-sided shapes. The learning trajectory includes (1) students can collaboratively understand the surface area of the cube (2) collaboratively, students can understand the space diagonal of a block. With the existence of LSLC, researchers can form learning communities with research subjects, collaborate in making learning designs and teaching materials, and produce multilevel effective learning through sharing tasks and jumping tasks Â

Mathematics is generally considered a complex subject by the majority of students in Indonesia. Students tend to rely on simple learning strategies such as memorizing formulas. This perpetual trend distance our students from deeper mathematical understandings such as concept application. In this study, we develop an interactive learning media based on Microsoft PowerPoint to instill a deep conceptual understanding of polyhedrons in class VIII students. This Research and Development study follows the 4D development model with a limited dissemination phase. The research data was collected through validation techniques by expert validators to measure the feasibility level of learning media. The instruments used in the research were interview sheets, observation sheets, learning style tests, media validation sheets, language validation sheets, and material validation sheets. The data analysis technique uses the Method of Summated Ratings, then the eligibility percentage for the developed media is calculated. The results showed that the eligibility percentage for media experts was 92%, material experts 96%, and linguists 90%. The average percentage of the three assessments corresponds to the “very valid” category. In conclusion, the media developed is very feasible for its intended purpose.

Crystallization of organic steric molecules often leads to multiple polyhedral crystal morphologies. However, the relationships among the molecular structure, supramolecular interaction, aggregation mode and crystal morphology are still unclear. In this work, we elaborate two model crystals formed by spiro[fluorene‐9,9′‐xanthene] (SFX) and spiro[cyclopenta[1,2‐b : 5,4‐b′]dipyridine‐5,9′‐xanthene] (SDAFX) to demonstrate the feasibility of morphology prediction by periodic bond chain (PBC) theory based on interaction energy (IE) values in terms of single point energy. With non‐directional van der Waals forces, only one PBC direction is found in SFX crystal, leading to the irregular 1D rod‐like structure. Compared with SFX, the extra N heteroatoms in SDAFX can bring additional hydrogen bonds and some other interactions into the bulky molecular skeletons, inducing 3‐dimensionally oriented PBCs to form the explicit F‐face network in SDAFX which leads to the final octahedral structure. A simple and accurate method has been provided to quantify PBC vector on the supramolecular level in the organic molecular system, and the PBC theory has also been further demonstrated and developed in the morphology prediction of organic spiro‐molecules. [ABSTRACT FROM AUTHOR]

We provide closed-form expressions for the first moments (i.e., the volume and volume-weighted centroid) of a polyhedron clipped by a paraboloid, that is, of a polyhedron intersected with the subset of the three-dimensional real space located on one side of a paraboloid. These closed-form expressions are derived following successive applications of the divergence theorem and the judicious parametrization of the intersection of the polyhedron's faces with the paraboloid. We provide means for identifying ambiguous discrete intersection topologies, and propose a corrective procedure for preventing their occurrence. Finally, we put our proposed closed-form expressions and numerical approach to the test with millions of random and manually engineered polyhedron/paraboloid intersection configurations. The results of these tests show that we are able to provide robust machine-accurate estimates of the first moments at a computational cost that is within one order of magnitude of that of state-of-the-art half-space clipping algorithms. [ABSTRACT FROM AUTHOR]

Antinorms (homogeneous concave functionals on a cone) have many applications in functional analysis, matrix theory, etc. Some duality theory results, like Young's inequality, the Fenchel–Moreau theorem, and others, carry over to antinorms. The essential difference is however the existence of infinitely many nontrivial self-dual antinorms, whereas only the Euclidean norm has this property among convex norms. The unit ball of a self-dual antinorm is a self-polar set (i.e., a set with its polar). The complete classification of self-dual antinorms in is available which includes piecewise-linear (polyhedral) antinorms. The existence of these antinorms in higher dimensions was stated as an open problem in 2021. This article presents some construction of polyhedral antinorms in for . The unit balls of the antinorms (i.e., self-polar infinite polyhedra) can have arbitrary prescribed numbers of vertices. [ABSTRACT FROM AUTHOR]

Many authors have been studied on the relations between Minkowski geometry and convex solids especially polyhedra. In this paper we introduce two new Minkowski geometries derived by dTPD--metric and dTTI--metric which unit spheres are truncated pentakis dodecahedron and truncated triakis icosahedron, respectively. These solids are in the class Truncated Catalan solids. We also give some properties of dTPD--metric and dTTI--metric and we show that the group of isometries of the 3--dimensional space covered by dTPD--metric or dTTI--metric is the semi-direct product of icosahedral group Ih the (Euclidean) symmetry group of the icosahedron and T(3) the group of all translations of the 3--dimensional space. [ABSTRACT FROM AUTHOR]

Copyright of Jurnal Pendidikan Indonesia is the property of Publikasi Indonesia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The ability that students must have is the ability of mathematical representation. This research aims to determine if eighth-grade students at Al-Qona'ah Islamic Junior High School improve their mathematical representation skills after using the Edpuzzle application to learn how to construct polyhedrons. It was a quantitative research design using the Quasi Experiment research method with control and experimental classes. This research's population comprised 60 students (23 males and 37 females). After conducting research, it was determined that students' mathematical representation abilities did not improve with the aid of the Edpuzzle application on the polyhedron due to the need for more learning support facilities when utilizing the Edpuzzle application. This research is supported by the t-test, which yielded t-count t-table or -29.2936 -1.67155 so that H0 is accepted. The results of the n-gain calculation yielded a total n-gain score of 0.03, or the n-gain was low, indicating was no progress in learning using the Edpuzzle application on the polyhedron. This study did not have an impact on increasing students' mathematical representation.

Pope Francis is able to communicate common values across borders of religion, regions, and sociopolitical systems. Catholic social teaching on the common good, particularly as articulated and promoted by him as part of a culture of encounter, conveys a relevant message for our times. Approaching the pope's initiative from a South Asian context, I argue that an engagement with dharma, a religioethical vision, can be part of this culture of encounter, especially in public theological conversations about the common good. Specifically, the themes of the common good, like integral ecology and care for the vulnerable, as earnestly promoted by Pope Francis, can converse with dharma for mutual enrichment, even while the basic teachings on human dignity, freedom, and inalienable rights can usefully enrich the latter. [ABSTRACT FROM AUTHOR]

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Because of their large volume variation and inferior electrical conductivity, Mn3O4-based oxide anode materials have short cyclic lives and poor rate capability, which obstructs their development. In this study, we successfully prepared a Mn3O4/N-doped honeycomb carbon composite using a smart and facile synthetic method. The Mn3O4 nanopolyhedra are grown on N-doped honeycomb carbon, which evidently mitigates the volume change in the charging and discharging processes but also improves the electrochemical reaction kinetics. More importantly, the Mn—O—C bond in the Mn3O4/N-doped honeycomb carbon composite benefits electrochemical reversibility. These features of the Mn3O4/N-doped honeycomb carbon (NHC) composite are responsible for its superior electrochemical performance. When used for Li-ion batteries, the Mn3O4/N-doped honeycomb carbon anode exhibits a high reversible capacity of 598 mAh·g−1 after 350 cycles at 1 A·g−1. Even at 2 A·g−1, the Mn3O4/NHC anode still delivers a high capacity of 472 mAh·g−1. This work provides a new prospect for synthesizing and developing manganese-based oxide materials for energy storage. [ABSTRACT FROM AUTHOR]

In this paper, we investigate properties concerning some recently introduced finite coarse shape invariants—the k-th finite coarse shape group of a pointed topological space and the k-th relative finite coarse shape group of a pointed topological pair. We define the notion of finite coarse shape group sequence of a pointed topological pair X , X 0 , x 0 as an analogue of homotopy and (coarse) shape group sequences and show that for any pointed topological pair, the corresponding finite coarse shape group sequence is a chain. On the other hand, we construct an example of a pointed pair of metric continua whose finite coarse shape group sequence fails to be exact. Finally, using the aforementioned pair of metric continua together with a pointed dyadic solenoid, we show that finite coarse-shape groups, in general, differ from both shape and coarse-shape groups. [ABSTRACT FROM AUTHOR]

The article presents a method for constructing the common perpendicular of two skew lines in a given polyhedron.The method is based on constructing the intersecting line of two planes that are respectively perpendicular to the two skew lines. The common perpendicular is constructed parallel to this line so that it intersects the skew lines. Examples of constructing the common perpendicular of skew lines in a cube, a right triangular prism, and a regular tetrahedron are considered. [ABSTRACT FROM AUTHOR]

Let n≥3 $n\ge 3$ and Rn ${R}_{n}$ be a 3‐polytopal graph such that for every 3≤i≤n $3\le i\le n$, Rn ${R}_{n}$ has at least one vertex of degree i $i$. We find the minimal vertex count for Rn ${R}_{n}$. We then describe an algorithm to construct the graphs Rn ${R}_{n}$. A dual statement may be formulated for faces of 3‐polytopes. The ideas behind the algorithm generalise readily to solve related problems. Moreover, given a 3‐polytope Tl ${T}_{l}$ comprising a vertex of degree i $i$ for all 3≤i≤l $3\le i\le l$, l $l$ fixed, we define an algorithm to output for n>l $n\gt l$ a 3‐polytope Tn ${T}_{n}$ comprising a vertex of degree i $i$, for all 3≤i≤n $3\le i\le n$, and such that the initial Tl ${T}_{l}$ is a subgraph of Tn ${T}_{n}$. The vertex count of Tn ${T}_{n}$ is asymptotically optimal, in the sense that it matches the aforementioned minimal vertex count up to order of magnitude, as n $n$ gets large. In fact, we only lose a small quantity on the coefficient of the second highest term, and this quantity may be taken as small as we please, with the tradeoff of first constructing an accordingly large auxiliary graph. [ABSTRACT FROM AUTHOR]

Here, we considerably develop the methods of power geometry for a system of partial differential equations and apply them to two different fluid dynamics problems: computing the boundary layer on a needle in the first approximation and computing the asymptotic forms of solutions to the problem of evolution of the turbulent flow. For each equation of the system, its Newton polyhedron and its hyperfaces with their normals and truncated equations are calculated. To simplify the truncated systems, power-logarithmic transformations are used and the truncated systems are further extracted. Here, we propose algorithms for computing unimodular matrices of power transformations for differential equations. Results: (1) the boundary layer on the needle is absent in liquid, while in gas it is described in the first approximation; (2) the solutions to the problem of evolution of turbulent flow have eight asymptotic forms, presented explicitly. [ABSTRACT FROM AUTHOR]

Backround. In the synthesis of complex compounds, the study of metallocomplexes containing ligands with N, O - donor centers is of particular importance. Knowing about them solves the problem of competing coordination in coordination chemistry. Purpose. Development of optimal synthesis conditions, determination of the structure and composition of the complex compound of zinc nitrate with formamideand nicotinamide. Study of the thermal properties of zinc nitrate complex compound with mixed ligands.. Methodology. Differential thermal analysis, elemental analysis, quantum-chemical calculations. Originality. For the first time, a new coordination compound of zinc nitrate with formamide and nicotinamide was synthesized. The methods of coordination of ligands and the geometry of the coordination ring in the synthesized complex compound, the formation energy of the complex, the bond length and the distribution of atomic charges were studied based on several options, and the most optimal option was obtained. The thermal properties and thermolysis products of the synthesized complex were studied. Findings. Molecules of formamide, nicotinamide and a complex compound, on the basis of data on the length of bonds and the distribution of charges on atoms, participate in the formation of a compound, the composition [ZnL1∙L6∙(NO3)2]∙H2O. During its thermolysis, the products were studied in the temperature ranges. [ABSTRACT FROM AUTHOR]

Given a graph G = (V , E) and an integer k ≥ 1 , the graph H = (V , F) , where F is a family of elements (with repetitions allowed) of E, is a k-edge-connected spanning subgraph of G if H cannot be disconnected by deleting any k - 1 elements of F. The convex hull of incidence vectors of the k-edge-connected subgraphs of a graph G forms the k-edge-connected subgraph polyhedron of G. We prove that this polyhedron is box-totally dual integral if and only if G is series–parallel. In this case, we also provide an integer box-totally dual integral system describing this polyhedron. [ABSTRACT FROM AUTHOR]

The primary objective of this study is to propose the use of nonlinear functions to find a feasible interior point in a region defined by the constraints of linear programming problems with the advantage of not having to use slack or surplus variables. The feasible region of linear programming problems is defined by convex sets named polyhedra that have the form Ax ≤ b and that can be bounded or unbounded. Finding an interior point (even extreme or frontier point) is not a trivial issue but is a necessary condition to initialize algorithms for solving a linear programming problem. To achieve this, unrestricted nonlinear penalty functions are applied and optimized. As a result, it is demonstrated that the optimal solution point corresponds to an interior point of the original polyhedron. It is concluded that the proposed algorithmic procedure possesses features that provide advantages for solving linear programming problems. [ABSTRACT FROM AUTHOR]

Molecular dynamics is used to study the filling of an anode with lithium. The anode is a defective two-layer silicene on a thin silicon carbide substrate. Lithium ions are deposited from numerous places above the top sheet of the silicene perpendicular to its plane. Bi-, tri-, and hexavacancies serve as defects in the silicene. The silicene sheets deform during lithium intercalation, but the structure of the silicene is retained. None of the defects change their shape appreciably after intercalation is complete. The structure of the SiC substrate is investigated by constructing simplified polyhedra separately for the Si and C subsystems. The C subsystem in crystalline silicon carbide is found to be more disordered than the Si subsystem. It is shown that the type of vacancies in silicene has no appreciable effect on the structure of the substrate. It is concluded that the vertical filling of the anode with lithium can be done when using a combination of silicene and silicon carbide as the anode material of a lithium-ion battery. [ABSTRACT FROM AUTHOR]

Background. The objects of study are triangulated compact polyhedron P , which are n -dimensional manifolds with boundary. The goal is to create new efficient algorithms for calculating modulo 2 intersection indices. Materials and methods. The construction of a closed n-dimensional path along a given absolute one-dimensional cycle is used. Results. An algorithm has been developed to calculate the intersection index of a given absolute one-dimensional cycle with an arbitrary relative cycle of dimension (n −1) . A rigorous mathematical justification of the algorithm is given. Conclusions. For the problem under consideration, the solution algorithm was developed for the first time. Its computational complexity is O(n2N + m), where n is the dimension of the manifold P , N is the number of its n -dimensional simplices, and m is the number of edges that make up the cycle x .

We give effective lower and upper bounds on the maximal generating degree d (I n ¯) and the Castelnuovo–Mumford regularity reg (I n ¯) of the integral closure of a power I n of a monomial ideal I for all n and determine the leading coefficient of the asymptotically linear functions d (I n ¯) and reg (I n ¯) . A number n 0 is also given such that d (I n ¯) becomes a linear function of n when n ≥ n 0 . [ABSTRACT FROM AUTHOR]