Linear Order Research Articles

Adsorptive capture of fluoride ion from water by Co/Fe-LDH@Avocado kernel seeds biochar@Caboxymethylcellulose nanobiosorbent: Optimization, error function and multivariate analysis

The current investigation is devoted to synthesize a sustainable and effective nanobiosorbent by simple combination of cobalt-iron layered double hydroxide with avocado kernel seeds biochar and carboxymethyl cellulose to form a novel multifunctionalized Co/Fe-LDHs@AKS biochar@CMC material for adsorptive capture of fluoride under optimized conditions. The EDX analysis referred to 42.7 %(C) 33.4 %(O), 14.3 %(Co) 5.3 %(Fe) 2.6 %(Na) 1.2 %(Cl) and 0.52 %(Mn). The highest adsorptive capture of fluoride ion by Co/Fe-LDH@AKS biochar@CMC) nanobiosorbent were at pH ≤ 2.0 and pH 7.0 due to ion-pair interaction and anion exchange mechanisms. The fluoride removal achieved 90.9–100.0 % upon using 100 mg of Co/Fe-LDH@AKS biochar@CMC. The modeled data by four linear and non-linear expressions confirmed the highest average relative error (ARE) by the non-linear Jovanovich (ARE = 4.66) and linear Jovanovich (ARE = 12.69). The kinetic study ascertained that the adsorptive capturing reaction of fluoride ion was best fitted to both linear and nonlinear pseudo 2nd order.

The adjoint map of Euclidean plane curves and curvature problems

The adjoint map of a pair of naturally parametrized curves in the Euclidean plane is studied from the point of view of the curvature. A main interest is when the given curve and its adjoint curve share the same natural parameter and the same curvature. For the general linear second order differential equation we introduce a function expressing the deformation of curvatures induced by the adjoint map.

Small ordered theories and quasi-successor properties on 1-type

The article is dedicated to the properties of 1-types in small ordered theories, specifically focusing on a particular generalization of the concept of a successor function on integers known as a quasi-successor. The article includes examples of 1-types, present in both discrete and dense orders, on which the 2-formula φ(x, y) acts, which is a quasi-successor. For the first time, the concept of quasisuccessor was introduced by the authors in their previous works. The problems of properties and counting the number of countable models of theories with a definable linear order have been studied by many scientists, among them L. Mayer, S.V. Sudoplatov, B.Sh. Kulpeshov, B.S. Baizhanov, A. Alibek, T.S. Zambarnaya, S. Moconja and P. Tanovic. Formulas with properties of succession play an important role in the study of the case of maximal countable models. Using the compactness theorem for a non-isolated 1-type, it is possible to construct a model in which there is an infinite discrete order of the type ω* + ω. On this discrete order, a complete 1-type with the quasi-successor property can be distinguished. A complete description of the subclass of theories having the maximal countable spectrum opens p the possibility of describing a possible countable spectrum for theories with a definable linear order.

Hardness and approximation of submodular minimum linear ordering problems

AbstractThe minimum linear ordering problem (MLOP) generalizes well-known combinatorial optimization problems such as minimum linear arrangement and minimum sum set cover. MLOP seeks to minimize an aggregated cost $$f(\cdot )$$ f ( · ) due to an ordering $$\sigma $$ σ of the items (say [n]), i.e., $$\min _{\sigma } \sum _{i\in [n]} f(E_{i,\sigma })$$ min σ ∑ i ∈ [ n ] f ( E i , σ ) , where $$E_{i,\sigma }$$ E i , σ is the set of items mapped by $$\sigma $$ σ to indices [i]. Despite an extensive literature on MLOP variants and approximations for these, it was unclear whether the graphic matroid MLOP was NP-hard. We settle this question through non-trivial reductions from mininimum latency vertex cover and minimum sum vertex cover problems. We further propose a new combinatorial algorithm for approximating monotone submodular MLOP, using the theory of principal partitions. This is in contrast to the rounding algorithm by Iwata et al. (in: APPROX, 2012), using Lovász extension of submodular functions. We show a $$(2-\frac{1+\ell _{f}}{1+|E|})$$ ( 2 - 1 + ℓ f 1 + | E | ) -approximation for monotone submodular MLOP where $$\ell _{f}=\frac{f(E)}{\max _{x\in E}f(\{x\})}$$ ℓ f = f ( E ) max x ∈ E f ( { x } ) satisfies $$1 \le \ell _f \le |E|$$ 1 ≤ ℓ f ≤ | E | . Our theory provides new approximation bounds for special cases of the problem, in particular a $$(2-\frac{1+r(E)}{1+|E|})$$ ( 2 - 1 + r ( E ) 1 + | E | ) -approximation for the matroid MLOP, where $$f = r$$ f = r is the rank function of a matroid. We further show that minimum latency vertex cover is $$\frac{4}{3}$$ 4 3 -approximable, by which we also lower bound the integrality gap of its natural LP relaxation, which might be of independent interest.

A Basic Set of Cancellation Violating Sequences for Finite Two-Dimensional Non-Additive Measurement

Abstract Cancellation conditions play a central role in the representation theory of measurement for a weak order on a finite two-dimensional Cartesian product set X. A weak order has an additive representation if and only if it violates no cancellation conditions. Given X, a longstanding open problem is to determine the simplest set of cancellation conditions that is violated by every linear order that is not additively representable. Here, we report that the simplest set of cancellation conditions on a 5 by 5 product X is obtained.

Structural and spectroscopic investigation of 1-acetyl-2-(4-ethoxy-3-methoxyphenyl) cyclopropane and its NLO activity

To identify promising compounds and to develop a potent non-linear optical material, the molecule 1-acetyl-2-(4-ethoxy-3-methoxyphenyl) cyclopropane (AEMC) was selected. FTIR and FT-Raman spectroscopy techniques were employed to predict the functional groups and vibrational modes of AEMC. Gaussian 09 W software was utilised to analyse the parameters of the optimised title compound. Reactive sites were forecasted using MEP plots. To clarify the chemical significance of the molecule, ELF and LOL are utilised. Furthermore, the presence of interactions within the molecule is confirmed by RDG analysis. The strong and weak hydrogen bonds between the non-bonding atoms of AEMC are studied with the aid of AIM analysis. Additionally, the material's capacity to produce non-linear effects (NLO) was ascertained by examining the linear polarizability and first order hyper polarizability values.

Can we read stones? Quantifying the information loss in flintknapping

One of the methods of analysing the manufacturing process of lithic tools is by “reading” the scars of removals visible on the surface of cores or bifaces. The paper aims to review the limitations of this approach, by answering the question as to how much information from the original knapping process is still preserved in the cores and bifaces. To quantify the information loss we used experimentally knapped pieces, that we then refitted to check which removals are still visible on the surface of the analysed forms. We tested different measures of information loss in the context of removals and sequences of removals, but also the chronological relationship between sequences i.e. the number of linear extensions and missing nearest connections. On average, 39.9% of the original removals and 54.1% of the sequences of removals are preserved on the surface, but only 14.1% of the original relationships between sequences can be observed. Finally, we used simple machine learning to find an algorithm for estimating the loss of the nearest chronological relationships between sequences when no refits are available. Due to the extremely high information loss for the linear order of the knapping process we: a) propose to abandon these elements of the diacritic approach which aim to reconstruct the rhythms and schemes of knapping; b) evaluate the quality of the reconstructed knapping scheme (partial order) prior to further comparative analyses. Here we propose an algorithm to estimate the number of missing connections to test the quality of the knapping process while using diacritic schemes.

Параболічні крайові задачі математичної фізики в кусково-однорідному клиновидному циліндрично-круговому півпросторі з порожниною

The unique exact analytical solutions of parabolic boundary value problems of mathematical physics in piecewise homogeneous by the radial variable r wedge-shaped by the angular variable φ cylindrical-circular half-space with a cavity were constructed at first time by the method of classical integral and hybrid integral transforms in combination with the method of main solutions (matrices of influence and Green matrices) in the proposed article. The cases of assigning on the verge of the wedge the boundary conditions of the 1st kind (Dirichlet) and the 2nd kind (Neumann) and their possible combinations (Dirichlet – Neumann, Neumann – Dirichlet) are considered. Finite integral Fourier transform by an angular variable, a finite integral Fourier transform on the Cartesian semiaxis (0; +∞) by an applicative variable z and a Weber hybrid integral transform type on the polar axis (R0; +∞) with n points of conjugation by a radial variable were used to construct solutions of investigated boundary value problems. The consistent application of integral transforms by geometric variables allows us to reduce the three-dimensional initial boundary-value problems of conjugation to the Cauchy problem for a regular linear inhomogeneous 1st order differential equation whose unique solution is written in a closed form. The consistent application of inverse integral transforms to the obtained solution in the space of images restores the solutions of the considered parabolic boundary value problems through their integral image in an explicit form in the space of the originals. At the same time, the main solutions to the problems were obtained in an explicit form.

Computability Theory: Constructive Applications of the Lefthanded Local Lemma and Characterizations of Some Classes of Cohesive Powers

AbstractThe Lovász local lemma (LLL) is a technique from combinatorics for proving existential results. There are many different versions of the LLL. One of them, the lefthanded local lemma, is particularly well suited for applications to two player games. There are also constructive and computable versions of the LLL. The chief object of this thesis is to prove an effective version of the lefthanded local lemma and to apply it to effectivise constructions of non-repetitive sequences.The second goal of this thesis is to categorize some classes of cohesive powers. We completely describe both the isomorphism types of cohesive powers of equivalence structures and injection structures, as well as clarify the relationship between these cohesive powers and their original structures. We also describe the finite condensation of cohesive powers of computable copies of the integers as a linear order by cohesive sets whose complement are computably enumerable.Finally, we investigate the possibility of decomposing problems in the Weihrauch degrees into a product of first order part and second order part. We give a preliminary result in this direction.Abstract prepared by Daniel Mourad.E-mail: daniel.mourad@uconn.eduURL: https://daniel-mourad.scholar.uconn.edu/wp-content/uploads/sites/2530/2023/06/ThesisFinalWithRevisions-2.pdf

A Novel Fitted Method for a Class of Singularly Perturbed Differential-Difference Equations with Small Delay Exhibiting Twin Layer or Oscillatory Behaviour

A new exponentially fitted three term method is developed for the numerical treatment of a class of linear second order singularly perturbed differential-difference equations (SPDDEs) which involves the small delay in un-differentiated term. The solution of such equations with the interval and boundary conditions exhibits twin layer or oscillatory behaviour. The method uses the Taylor’s series expansion for constructing an equivalent valid version of the original problem first and then, to derive a new three term finite difference recurrence relationship/scheme. The non-uniformity in the solution is resolved by the introduction of a suitable fitting parameter in the derived new scheme. Finally the resulting system of algebraic equations is solved by the well known “discrete invariant algorithm.” Method is analyzed for the stability and convergence, and the theory is illustrated by solving several test example problems. Computational results are tabulated and compared to show the applicability, accuracy and efficiency of the method. Theory and computation show that the method is able to approximate the solution very well with second order convergence rate.

Ordered Groups, Computability and Cantor-Bendixson Rank

AbstractWe study ordered groups in the context of both algebra and computability. Ordered groups are groups that admit a linear order that is compatible with the group operation. We explore some properties of ordered groups and discuss some related topics. We prove results about the semidirect product in relation to orderability and computability. In particular, we give a criteria for when a semidirect product of orderable groups is orderable and for when a semidirect product is computably categorical. We also give an example of a semidirect product that has the halting set coded into its multiplication structure but it is possible to construct a computable presentation of this semidirect product.We examine a family of orderable groups that admit exactly countably many orders and show that their space of orders has arbitrary finite Cantor–Bendixson rank. Furthermore, this family of groups is also shown to be computably categorical, which in particular will allow us to conclude that any computable presentation of the groups does not admit any noncomputable orders. Lastly, we construct an example of an orderable computable group with no computable Archimedean orders but at least one computable non-Archimedean order.Abstract prepared by Waseet Kazmi.E-mail: waseet.kazmi@uconn.eduURL: http://hdl.handle.net/11134/20002:860745910

Sparse optimal control of Timoshenko's beam using a locking‐free finite element approximation

AbstractThis paper addresses the optimal control problem with sparse controls of a Timoshenko beam, its numerical approximation using the finite element method, and the numerical solution via nonsmooth methods. Incorporating sparsity‐promoting terms in the cost function is practically useful for beam vibration models and results in the localization of the control action that facilitates the placement of actuators or control devices. We consider two types of sparsity‐inducing penalizers: the ‐norm and the ‐penalizer, which measures function support. We analyze discretized problems utilizing linear finite elements with a locking‐free scheme to approximate the states and adjoint states. We confirm that this approximation has the looking‐free property required to achieve a linear convergence linear order of approximation for control case and depending on the set of switching points in the controls. This is similar to the purely ‐norm penalized optimal control, where the order of approximation is independent of the thickness of the beam.

Novel applications of oustaloup recursive approximation and modified oustaloup recursive approximation methods in linear fractional order control design

Novel applications of oustaloup recursive approximation and modified oustaloup recursive approximation methods in linear fractional order control design

Pseudopartitive constructions are not a subtype of nominal juxtaposition in Beserman

Abstract Juxtaposition as a machinery of building noun phrases is well-known to be widespread in Uralic languages: the modifier is left-adjoined to the head and does not bear any morphological marker of syntactic dependency. This strategy is used to attach adjectives, cardinals and modifying nominals to nouns (like in Beserman ǯ́aǯ́eg siĺ ‘goose meat’), and to build constructions with measure nouns (like Beserman odig kə̑də̑ gibi ‘one basket of mushrooms’, lit. one basket mushroom). However, there remains a question whether all these constructions share the same syntactic structure. We consider pseudopartitive constructions with measure nouns in comparison with NPs containing non-marked modifying nominals and NPs with adjectives, showing that they do not share the same syntactic structure. Constructions with unmarked modifying nominals show properties of compounding, while pseudopartitives arguably have a measure phrase (a cardinal with a measure noun) and a noun phrase (the quantified nominal), which is the head of the pseudopartitive construction. The syntactic properties we analyze include constituent properties, branching, pronominalization, fragment questions, linear ordering restrictions, particular properties of head ellipsis, and information structure effects.

Linear listing order and hierarchical classification: history, conflict, and use

Taxonomic criteria alone are not sufficient to determine a linear sequence for the arrangement of collection specimens according to a preferred classification or the linear sequence according to which taxa are best discussed in articles or books. The choice of methodology to obtain a linear sequence of taxa in agreement with a hierarchical classification has been little studied and remains controversial. In this article, I offer an historical background, before examining properties, use and limits of possible listing criteria. The result of a linearization effort depends on arbitrary choices with respect to two aspects of the hierarchical classification we intend to linearize. One is the order to be followed in listing the immediately subordinate members of a given taxon, the other is the choice of the sets of taxa to be linearized according to tradition, alphabetic order or other criterion. The example presented here, related to the “orders” of Hexapoda, demonstrates the need to specify very clearly the extent and composition of the uncollapsed classification backbone retained in the linearization procedure.

How Abstract Is Linguistic Generalization in Large Language Models? Experiments with Argument Structure

Abstract Language models are typically evaluated on their success at predicting the distribution of specific words in specific contexts. Yet linguistic knowledge also encodes relationships between contexts, allowing inferences between word distributions. We investigate the degree to which pre-trained transformer-based large language models (LLMs) represent such relationships, focusing on the domain of argument structure. We find that LLMs perform well in generalizing the distribution of a novel noun argument between related contexts that were seen during pre-training (e.g., the active object and passive subject of the verb spray), succeeding by making use of the semantically organized structure of the embedding space for word embeddings. However, LLMs fail at generalizations between related contexts that have not been observed during pre-training, but which instantiate more abstract, but well-attested structural generalizations (e.g., between the active object and passive subject of an arbitrary verb). Instead, in this case, LLMs show a bias to generalize based on linear order. This finding points to a limitation with current models and points to a reason for which their training is data-intensive.1

Silver, copper, and cobalt trimetallic nanoparticles; synthesis, characterization and its application as adsorbent for acid blue 7 dye

Abstract The synergistic effects of metal complex nanoparticles in remediation of environment had opened a versatile field of research as providing differential attractive forces for a given pollutant on their surfaces. Herein, trimetallic nanoparticles of silver, copper and cobalt (Ag–Cu–Co TNPs) were prepared via chemical reduction method using sodium borohydride as reductant which were then characterized through SEM, EDX, XRD and FT-IR analytical techniques. As model dye, acid blue 7 was adsorbed on the surface of fabricated particles utilizing batch adsorption approach. The adsorption conditions like temperature, adsorbent dosage, pH, and contact time were optimized to get maximum adsorption of the selected dye which were; 333 K, 0.01 g, pH 6 and 30 min respectively. The adsorption data were analyzed using kinetic and isotherm models, with the linear pseudo 2nd order kinetics and Langmuir models being the most suitable. The maximum adsorption capacity at 333 K was found to be 74.07 mg/g. Thermodynamic variables such as entropy (ΔS°), enthalpy (ΔH°), and Gibbs free energy (ΔG°) changes were calculated to understand the adsorption feasibilities. Results indicated that the adsorption process was endothermic (ΔH° = 6.867 KJ mol−1) and spontaneous ΔG° (J mol−1) −219.2, −702.9 and −1086.6 at 293 K, 313 K and 333 K respectively. The entropy change (ΔS° = 24.185 J mol−1 K−1) suggested an increased disorder at the solid–solution interface during adsorption.

Fundamental power of the city – A proposition of a new paradigm and index for city development

Managing a dynamic and complex urban system according to the single concept of city development is insufficient. The study's aim is to present the main concepts of cities development, formulate a new hybrid concept of city, and propose a related index to support strategy implementation and monitoring. The research methods include literature scoping, literature content analysis, and linear ordering as a multivariate method of analysis. The research conclusion identifies a new hybrid concept of a “resilient smart sustainable city” and explains a distinction between weak and strong perception of the concept. The practical part of the research develops synthetic measure “Fundamental Power of the City Index” which allows to select variables representing individual cities' priorities and apply them in every city analysis, development strategy building, and monitoring. The Index is tested for 18 voivodship cities in Poland for the period 2014–2020. The results of this study can support city stakeholders in their efforts in developing “resilient smart sustainable city”.

Attraction Versus Repulsion Between Doublons or Holons in Mott-Hubbard Systems

For the Mott insulator state of the Fermi-Hubbard model in the strong-coupling limit, we study the interaction between quasi-particles in the form of doublons and holons. Comparing different methods – the hierarchy of correlations, strong-coupling perturbation theory, and exact analytic solutions for the Hubbard tetramer – we find an effective interaction between doublons and/or holons to linear order in the hopping strength which can display attractive as well as repulsive contributions, depending on the involved momenta. Finally, we speculate about the implications of our findings for high-temperature superconductivity.

A bio-medical snake optimizer system driven by logarithmic surviving global search for optimizing feature selection and its application for disorder recognition

Abstract It is of paramount importance to enhance medical practices, given how important it is to protect human life. Medical therapy can be accelerated by automating patient prediction using machine learning techniques. To double the efficiency of classifiers, several preprocessing strategies must be adopted for their crucial duty in this field. Feature Selection (FS) is one tool that has been used frequently to modify data and enhance classification outcomes by lowering the dimensionality of datasets. Excluded features are those that have a poor correlation coefficient with the label class, i.e., they have no meaningful correlation with classification and do not indicate where the instance belongs. Along with the recurring features, which show a strong association with the remainder of the features. Contrarily, the model being produced during training is harmed, and the classifier is misled by their presence. This causes overfitting and increases algorithm complexity and processing time. The pattern is made clearer by FS, which also creates a broader classification model with a lower chance of overfitting in an acceptable amount of time and algorithmic complexity. To optimize the FS process, building wrappers must employ metaheuristic algorithms as search algorithms. The best solution, which reflects the best subset of features within a particular medical dataset that aids in patient diagnosis, is sought in this study using the Snake Optimizer (SO). The swarm-based approaches that SO is founded on have left it with several general flaws, like local minimum trapping, early convergence, uneven exploration and exploitation, and early convergence. By employing the cosine function to calculate the separation between the present solution and the ideal solution, the logarithm operator was paired with SO to better the exploitation process and get over these restrictions. In order to get the best overall answer, this forces the solutions to spiral downward. Additionally, SO is employed to put the evolutionary algorithms’ preservation of the best premise into practice. This is accomplished by utilizing three alternative selection systems – tournament, proportional, and linear – to improve the exploration phase. These are used in exploration to allow solutions to be found more thoroughly and in relation to a chosen solution than at random. These are Tournament Logarithmic Snake Optimizer (TLSO), Proportional Logarithmic Snake Optimizer, and Linear Order Logarithmic Snake Optimizer. A number of 22 reference medical datasets were used in experiments. The findings indicate that, among 86% of the datasets, TLSO attained the best accuracy, and among 82% of the datasets, the best feature reduction. In terms of the standard deviation, the TLSO also attained noteworthy reliability and stability. On the basis of running duration, it is, nonetheless, quite effective.