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Recently, some new sequence spaces ℓ p (A α) (0 < p < ∞) , c 0 (A α) , c (A α) , and ℓ ∞ (A α) have been studied by Yaying et al. (Forum Math., 2024, https://doi.org/10.1515/forum-2023-0138) as matrix domains of A α = (a n , v α) , where a m , v α = { v α ρ (α) (m) , v ∣ m , 0 , v ∤ m , and ρ (α) (m) : = sum of the α th power of the positive divisors of m ∈ N . They obtained their duals, matrix transformations and associated compact matrix operators for these matrix classes. This article deals with some geometric properties of these sequence spaces. [ABSTRACT FROM AUTHOR]

A recent paper shows that in gene expression space the manifold spanned by normal tissues and the manifold spanned by the corresponding tumors are disjoint. The statement is based on a two-dimensional projection of gene expression data. In the present paper, we show that, for the multi-dimensional vectors defining the centers of cloud samples: 1. The closest tumor to a given normal tissue is the tumor developed in that tissue, 2. Two normal tissues define quasi-orthogonal directions, 3. A tumor may have a projection onto its corresponding normal tissue, but it is quasi-orthogonal to all other normal tissues, and 4. The cancer manifold is roughly obtained by translating the normal tissue manifold along an orthogonal direction defined by a global cancer progression axis. These geometrical properties add a new characterization of normal tissues and tumors and may have biological significance. Indeed, normal tissues at the vertices of a high-dimensional simplex could indicate genotype optimization for given tissue functions, and a way of avoiding errors in embryonary development. On the other hand, the cancer progression axis could define relevant pan-cancer genes and seems to be consistent with the atavistic theory of tumors. [ABSTRACT FROM AUTHOR]

Abstract Recently, some new sequence spaces ℓ p ( A α ) $\ell _{p}(\mathfrak{A}^{\alpha })$ ( 0 < p < ∞ ) $(0< p

Timber–concrete composite (TCC) structural systems are characterized by the combination of timber and concrete, which are connected to transmit shear forces between the two elements. In addition, to achieve an efficient connection, the slip between the two materials should be limited. Therefore, the load-carrying capacity, the stiffness, and the failure mode of TCC connections are important for the behavior of the composite element. This work aims to investigate the influence of test conditions on TCC connections using shear tests to determine the mechanical properties of connections. Therefore, it is essential to understand the influence of the configuration of the specimens (symmetric as push-out tests or asymmetric as inclined tests), the type of interface between the timber and concrete, and the test procedure (static or cyclic load protocol) on the resulting load-carrying capacity, stiffness, and failure modes. This paper reviews experimental tests conducted on TCC shear connection specimens, using various configurations to assess the influence of the test specimen configuration, material interface, and testing protocol on the determination of the mechanical properties. [ABSTRACT FROM AUTHOR]

Landslides triggered by rainstorms and earthquakes are prominent geological hazards that exhibit distinctive spatial and morphological characteristics due to diverse instability mechanisms. However, studies on differences between the two types of landslides remain limited. In this study, we explored differences in location and geometric properties between rainstorm‐induced landslides in Qinzhou, Longchuan and Fukuoka and earthquake‐induced landslides in Lushan, Iburi and Kaikōura. We normalized the location of landslides across the slope and quantified the landslide polygons using four geometric properties. Findings revealed that both location and geometric properties are specific to landslide type and differ between them. Earthquake‐induced landslides are more common near the ridge of a slope, while rainstorm‐induced landslides are more frequent in the valley or near streams. The quantitative analysis of geometric properties showed that earthquake‐induced landslides are generally larger and have a more compact, rounded and less complex shape. The two landslide types present different hazards, particularly in their runout zones, where dispersion of materials occurs. Insights from our quantitative approach serve as a critical foundation for informed decision‐making in emergency scenarios and contribute to enhancing landslide hazard management. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we establish a novel category of sequence spaces ℓ p q λ $\ell _{p}^{q_{\lambda}}$ and ℓ ∞ q λ $\ell _{\infty}^{q_{\lambda}}$ by utlizing q-analogue Λ q $\Lambda^{q}$ of Λ-matrix. Our investigation outlines several topological characteristics and inclusion results of these newly introduced sequence spaces, specifically identifying them as BK-spaces. Subsequently, we demonstrate that these novel sequence spaces are of nonabsolute type and establish their isometric isomorphism with ℓ p $\ell _{p}$ and ℓ ∞ $\ell _{\infty}$ . Moreover, we obtain the α-, β-, and γ-duals of these sequence spaces. We further characterize the class ( ℓ p q λ , X ) $(\ell _{p}^{q_{\lambda}},X)$ of matrices, where X is any of the spaces ℓ ∞ $\ell _{\infty }$ , c, or c 0 $c_{0}$ . Lastly, our study delves into the exploration of specific geometric properties exhibited by the space ℓ p q λ $\ell _{p}^{q_{\lambda}}$ .

In this paper, we establish a novel category of sequence spaces ℓ p q λ and ℓ ∞ q λ by utlizing q-analogue Λ q of Λ-matrix. Our investigation outlines several topological characteristics and inclusion results of these newly introduced sequence spaces, specifically identifying them as BK-spaces. Subsequently, we demonstrate that these novel sequence spaces are of nonabsolute type and establish their isometric isomorphism with ℓ p and ℓ ∞ . Moreover, we obtain the α-, β-, and γ-duals of these sequence spaces. We further characterize the class (ℓ p q λ , X) of matrices, where X is any of the spaces ℓ ∞ , c, or c 0 . Lastly, our study delves into the exploration of specific geometric properties exhibited by the space ℓ p q λ . [ABSTRACT FROM AUTHOR]

Corrugated web steel systems, such as corrugated web girders (CWG) and beams (CWSB), have the potential to influence the modern construction industry due to their unique properties, including enhanced shear strength and reduced necessity for transverse stiffeners. Nevertheless, the lack of a rapid and accurate design approach still limits its wide applications. Recently, gene expression programming (GEP) has been employed to predict the shear capacity of cold-formed steel channels, demonstrating superior predictive accuracy and compliance with established standards. This study applies GEP to predict the shear capacity of sinusoidal CWSBs and optimizes its predictive performance by employing a systematic grid search to explore combinations of chromosomes, head sizes, gene counts, and linking functions. The process involved testing 19 different parameter combinations and more than 60 developed models. The findings include the sensitivity of the model's performance to gene count and the critical role of the linking function. The optimal model in the study, GEP13, achieved R² of 0.95, an RMSE of 100.5, and an MAE of 86.6 in the testing dataset with 150 chromosomes, a head size of 12, and four genes using a multiplication linking function [ABSTRACT FROM AUTHOR]

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Nowadays, 3D laser scanning technology is extensively employed in laboratory investigations of steel structural components, providing accurate geometric dimensions to reduce uncertainties caused by indeterminate geometry in experimental results. It is often used in conjunction with the Finite Element (FE) Method and analytical solutions, which are more accurate deterministic operators in the research on steel structures. However, establishing a common methodological framework for transferring or mapping 3D-scanned information into finite element models for complex steel structures with stability and fatigue risks remains an ongoing task. In light of this, this study has developed a 3D scanning platform capable of obtaining accurate geometric dimensions for various types of steel components. Different coordinate systems and point cloud mapping algorithms have been established for different types of components to construct actual finite element models with initial imperfections. The feasibility of the self-developed 3D scanning platform and finite element modelling has been validated through three experimental cases: weld details, steel girders, and cylindrical shells. The research findings demonstrate that the captured point cloud can be automatically processed and corrected using the developed algorithm. The scanned data can then be input into the numerical model using various mapping algorithms tailored to the specific geometric properties of the specimens. The differences between the experimental test results and the simulated results obtained from the 3D-scanned finite element models remain within a small range. The self-developed 3D scanning platform and finite element modelling technique effectively capture the actual dimensions of different steel components, enabling the prediction of their stability and fatigue risks through numerical simulations. [ABSTRACT FROM AUTHOR]

Timber–concrete composite (TCC) structural systems are characterized by the combination of timber and concrete, which are connected to transmit shear forces between the two elements. In addition, to achieve an efficient connection, the slip between the two materials should be limited. Therefore, the load-carrying capacity, the stiffness, and the failure mode of TCC connections are important for the behavior of the composite element. This work aims to investigate the influence of test conditions on TCC connections using shear tests to determine the mechanical properties of connections. Therefore, it is essential to understand the influence of the configuration of the specimens (symmetric as push-out tests or asymmetric as inclined tests), the type of interface between the timber and concrete, and the test procedure (static or cyclic load protocol) on the resulting load-carrying capacity, stiffness, and failure modes. This paper reviews experimental tests conducted on TCC shear connection specimens, using various configurations to assess the influence of the test specimen configuration, material interface, and testing protocol on the determination of the mechanical properties.

In this paper, we introduce the fibonomial sequence spaces ... and ..., and show that these are BKspaces. Also, we prove that these new spaces are linearly isomorphic to ℓp and ℓ∞. Moreover, we determine the α-, β -, γ -duals for these new spaces and characterize some matrix classes. The final section is devoted to the investigation of some geometric properties of the newly defined space ... . [ABSTRACT FROM AUTHOR]

In this paper, we introduce the fibonomial sequence spaces ... and ..., and show that these are BKspaces. Also, we prove that these new spaces are linearly isomorphic to ℓp and ℓ∞. Moreover, we determine the α-, β -, γ -duals for these new spaces and characterize some matrix classes. The final section is devoted to the investigation of some geometric properties of the newly defined space ... . [ABSTRACT FROM AUTHOR]

Near Surface‐Mounted Fiber Reinforced Polymer (NSM FRP) strips have become a popular technique for the rehabilitation of existing deteriorated concrete structures, the effectiveness of which is vitally related to its bond to concrete. The present Artificial Neural Network (ANN) model, aimed at providing precise predictions for bond strength, utilizes nearly 550 refined dataset points and accounts for more influential parameters, namely elastic modulus, cross‐sectional area, bond length of FRP strips, groove size, concrete edge distance, groove spacing, and concrete's compressive strength. The very few relevant publications for the prediction of bond strength between NSM FRP composites and concrete employing artificial intelligence bond models considered limited database sizes and few key parameters. The Matlab software was utilized to build, train, and test the network model using seven input variables and one targeted output. Detailed statistical analysis was presented to test the model's validity with Taylor charts produced using the Matlab software for the purpose of comparing the performance of the present model against different literature models. The proposed ANN model showed a high prediction ability and a low mean square error. Indeed, the mean square error for the testing and validation data remained below 0.00055, whereas the coefficient of determination exceeded 0.99. The error charts for training and testing database revealed normal distribution of bond strength residuals; supporting further the validity of the proposed model. The trending behavior of the ultimate bond force versus the key parameters was consistent with that captured in the various literature models. The statistical and the sensitively analyses performed stipulated the validity of the present model for producing reliable prediction for bond strength between NSM FRP strips and concrete. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce a new regular matrix B ~ and define the sequence space ℓ p ( B ~ ). We also examine some topological properties for this space and determine α - , β - , γ - duals. As well, we characterize some matrix classes and investigate some geometric properties such as uniform convexity, strict convexity and super-reflexivity. [ABSTRACT FROM AUTHOR]

We develop some new sequence spaces p (P (q)) and ∞ (P (q)) by using q-Pascal matrix P (q). We discuss some topological properties of the newly defined spaces, obtain the Schauder basis for the space p (P (q)) and determine the Alpha-(α -), Beta-(β -) and Gamma-(γ -) duals of the newly defined spaces. We characterize a certain class ( p (P (q)) , X) of infinite matrices, where X ∈ { ∞ , c , c 0 } . Furthermore, utilizing the proposed results, we characterize certain other classes of infinite matrices. We also examine some geometric properties, like the approximation property, Dunford–Pettis property, Hahn–Banach extension property, and Banach–Saks-type p property of the spaces p (P (q)) and ∞ (P (q)) . [ABSTRACT FROM AUTHOR]

The paper considers ray transforms of the moments of symmetric tensor fields of arbitrary rank given in the unit disk. The basic geometric and differential properties of mixed ray transforms of tensor fields and mixed ray transforms of the moments of tensor fields are established. A simple algorithm for reconstructing a low-rank tensor field from known mixed ray transforms of its moments is proposed and justified. [ABSTRACT FROM AUTHOR]

In this article we introduce the Riesz difference sequence space rpq(ΔBα) of fractional order α, defined by the composition of fractional backward difference operator ΔBα given by (ΔBαv)k = ... and the Riesz matrix Rq. We give some topological properties, obtain the Schauder basis and determine the α-, β- and γ- duals and investigate certain geometric properties of the space rpq(ΔBα). Finally, we characterize certain classes of compact operators on the space rpq(ΔBα) using Hausdorff measure of non-compactness. [ABSTRACT FROM AUTHOR]

The objective of the study was to determine the geometric, gravimetric, aerodynamic, and frictional properties of maize grain as affected by varietal differences and moisture content. Honampa, Omankwa, Abontem, Timtim, and Obatanpa were the five maize grain varieties studied. Moisture content, geometric properties, gravimetric properties, aerodynamic properties, and frictional properties were studied. The geometric mean diameters ranged between 6.65 and 7.55 mm, while projected areas ranged between 52.98 and 73.12 m2. The surface area was between 139.69 and 180.29 mm2, and sphericity was from 0.71 to 0.80. The following ranges were obtained as thousand grain weight (213.74 and 292.89 g), and bulk density (709.50 and 746.00 kg/m3). The volume of a single seed was between 1.71 × 10−7 and 2.34 × 10−7 m3 while true density was 1250.0 kg/m3. Porosity ranged from 40.32% to 43.24% and terminal velocity ranged between 2.12 and 2.98 m/s. Drag coefficient of 7.18 to 14.60, drag force of 0.002 to 0.003, and Reynolds number between 992.71 and 1579.20 were similarly obtained. The static angle of repose varied with material surfaces while the dynamic angle of repose varied with grain variety. The grain demonstrated 19° static angle of repose, which portrays a very free flow. All the geometric properties increased with moisture besides sphericity although insignificant. The thousand grain weight, volume of single grain, and porosity increased with moisture content. Nonetheless, bulk density decreased and true density remained the same as moisture content increased. Terminal velocity, Reynolds number, and drag force increased as drag coefficient decreased with moisture content. The frictional properties increased with moisture content, and the Reynolds number was

Nowadays, 3D laser scanning technology is extensively employed in laboratory investigations of steel structural components, providing accurate geometric dimensions to reduce uncertainties caused by indeterminate geometry in experimental results. It is often used in conjunction with the Finite Element (FE) Method and analytical solutions, which are more accurate deterministic operators in the research on steel structures. However, establishing a common methodological framework for transferring or mapping 3D-scanned information into finite element models for complex steel structures with stability and fatigue risks remains an ongoing task. In light of this, this study has developed a 3D scanning platform capable of obtaining accurate geometric dimensions for various types of steel components. Different coordinate systems and point cloud mapping algorithms have been established for different types of components to construct actual finite element models with initial imperfections. The feasibility of the self-developed 3D scanning platform and finite element modelling has been validated through three experimental cases: weld details, steel girders, and cylindrical shells. The research findings demonstrate that the captured point cloud can be automatically processed and corrected using the developed algorithm. The scanned data can then be input into the numerical model using various mapping algorithms tailored to the specific geometric properties of the specimens. The differences between the experimental test results and the simulated results obtained from the 3D-scanned finite element models remain within a small range. The self-developed 3D scanning platform and finite element modelling technique effectively capture the actual dimensions of different steel components, enabling the prediction of their stability and fatigue risks through numerical simulations.

The texture analysis of cancer cells leads to a procedure to distinguish spatial differences within an image and extract essential information. This study used two test tumours images to determine cancer type, location, and geometric characteristics (area, size, dimensions, radius, etc.). The suggested algorithm was designed to detect and distinguish breast cancer using the segmentation-based threshold technique. The method of texture analysis Grey Level Size Zone method was used to extract 11 features: Small Zone Emphasis, Large Zone Emphasis, Low Grey Level Zone Emphasis, High Grey Level Zone Emphasis, Small Zone Low Grey Level Emphasis, Small Zone High Grey Level Emphasis, Large Zone Low Grey Level Emphasis, Large Zone High Grey Level Emphasis, Grey Level Non-Uniformity Normalized, Grey Level Non-Uniformity, and Zone Percentage. The results show that the tumuor's location is highly accurate depending on the extracting properties. The results of the suggested method give the decision to identify the type of tumours. The geometry of the tumour helps describe the tumour. [ABSTRACT FROM AUTHOR]

This article presents research activity by outstanding high school students aimed at discovering interesting geometric conservation properties in the context of Van Aubel's theorem, specifically in the case where the quadrilateral first degenerates into a triangle and later into a straight line. For some properties, proofs are presented with explanations of every stage. This activity was accompanied by computer software that facilitates dynamic research into various forms. [ABSTRACT FROM AUTHOR]

We develop some new sequence spaces 𝓁p(P(q)) and 𝓁∞(P(q)) by using q-Pascal matrix P(q). We discuss some topological properties of the newly defined spaces, obtain the Schauder basis for the space 𝓁p(P(q)) and determine the Alpha-(α-), Beta-(β-) and Gamma-(γ-) duals of the newly defined spaces. We characterize a certain class (𝓁p(P(q)),X) of infinite matrices, where X∈{𝓁∞,c,c0}. Furthermore, utilizing the proposed results, we characterize certain other classes of infinite matrices. We also examine some geometric properties, like the approximation property, Dunford–Pettis property, Hahn–Banach extension property, and Banach–Saks-type p property of the spaces 𝓁p(P(q)) and 𝓁∞(P(q)).

The Travelling Salesperson Problem (TSP) is a nondeterministic-polynomial hard (NP-hard) combinatorial problem that occurs in a wide range of industrial domains, including logistics, route finding, and computer wiring. Interestingly, despite the problem's inherent computational difficulty, when presented in Euclidean space (ETSP), human participants can produce close-to-optimal solutions in near-linear time. However, when asked to compare and select the most optimum solution from a set of pre-defined competing solution options, participants can struggle. In this study we investigate this paradox by asking participants to compare four closed-loop Euclidean TSP solutions, in order to determine which solution they perceived to have the most optimal tour cost. We hypothesise that the extracted geometric properties have an effect on stimulus selection in a discrimination task (selection or no selection). Accordingly, we extracted four geometric properties from competing stimuli in order to create a perceptual activation function. Predictive analytics demonstrated that a classification model could identify the most optimal solution 97% of the time using the perceptual activation scores alone, yet human participants only correctly determined the most optimal solution 47% of the time. Mixed-effects models suggest that 'likelihood of stimulus selection' can be modelled as a function of the weighted coefficients of competing perceptual activation scores within each trial; however only a small amount of the variance is explained by these perceptual activation scores. Finally, a drift–diffusion model was used to create a theoretical framework of how likelihood of stimulus selection is influenced by competing perceptual activators. Our study highlights a novel way of extracting and analysing the importance of geometric properties that influence ETSP discrimination tasks, and links this analysis to human behaviour when discriminating between competing ETSP solutions. [ABSTRACT FROM AUTHOR]

The application of concrete-filled stainless steel tubular (CFSST) columns has been increased rapidly in bridges and other infrastructure around the globe due to its greater corrosion resistance, fire resistance, and durability. This research has investigated the compressive behavior of CFSST columns both experimentally and numerically. An experimental program has been carried out with twenty-four (24) column specimens of six (6) different sizes and shapes with varying concrete strength. A 3D non-linear finite element model was developed to validate the experimental result. Besides, an extensive parametric study has been conducted to investigate the effect of geometric and material properties. It was observed that the numerical model can predict the experimental result and failure mode with very high accuracy. In general, the failure was occurred due to the outwards buckling of the steel tube. The ductility index decreased with increasing the compressive strength of concrete. The rectangular columns exhibited less ductility index than the square and circular columns. The increase in column axial capacity due to higher concrete strength was more significant for columns having a higher depth to thickness (D/t) ratio. Finally, the axial capacity of the columns was compared with the design standards. [ABSTRACT FROM AUTHOR]

Travel time is a measure of time taken to travel from one place to another. Global Positioning System (GPS) navigation applications such as Waze and Google Maps are easily accessible presently and allow users to plan a route based on travel time from one place to another. However, these applications can only estimate general travel time based on a vehicle's total distance and average safe speed without considering route curvature. A parametric cubic curve has shown a potential result in travel-time estimation through geometric properties. In this paper, travel time has been estimated using the curvature value obtained from the Hermite Interpolation curve fitted to each section of the selected road. Design speed is determined from the curvature value, and thus an algorithm for travel-time estimation incorporating initial driving information is developed. The proposed method's accuracy was compared to the existing method's accuracy using a real-life driving test. This comparison demonstrated that the proposed method estimates travel time more accurately than Google Maps and Waze. Future study can further improve the estimation by embedding traffic data into the algorithm. [ABSTRACT FROM AUTHOR]

It's appropriate mechanical behavior and its low carbon footprint allow bamboo to replace conventional construction materials in various applications. Currently, it should be considered that there are countries that still do not have sufficient knowledge about the structural characteristics of locally grown bamboos. In this sense, this research presents the results for the determination of the geometric properties and the compressive and tensile mechanical properties parallel to the fiber of the species Phyllostachys aurea from the Ecuadorian Amazon. With the samples tested, the compressive strength parallel to the fiber presented a minimum standard deviation in the results, showing an average strength of 52.4 MPa. After a statistical analysis of these values, a normal distribution was observed between them, increasing their reliability; the tensile strength parallel to the fiber showed a high standard deviation in the results, due to the difficulty in preparing the required sample as established in the standard ISO/FDIS - 22157 (2019). However, the average resistance of this parameter was 90.2 MPa, confirming that it is a bamboo with great potential against this type of load. Therefore, a comparison was made between the compressive and tensile strength of the Phyllostachys aurea species with other conventional materials used in construction such as reinforced concrete, structural steel and Guadua angustifolia Kunth bamboo. [ABSTRACT FROM AUTHOR]

Existing deep learning algorithms for point cloud analysis mainly concern discovering semantic patterns from the global configuration of local geometries in a supervised learning manner. However, very few explore geometric properties revealing local surface manifolds embedded in 3-D Euclidean space to discriminate semantic classes or object parts as additional supervision signals. This article is the first attempt to propose a unique multitask geometric learning network to improve semantic analysis by auxiliary geometric learning with local shape properties, which can be either generated via physical computation from point clouds themselves as self-supervision signals or provided as privileged information. Owing to explicitly encoding local shape manifolds in favor of semantic analysis, the proposed geometric self-supervised and privileged learning algorithms can achieve superior performance to their backbone baselines and other state-of-the-art methods, which are verified in the experiments on the popular benchmarks. [ABSTRACT FROM AUTHOR]

Abstract Background Epidermal growth factor receptor (EGFR) and its signaling pathways play a vital role in pathogenesis of lung cancer. By disturbing EGFR signaling, mutations of EGFR may lead to progression of cancer or the emergence of resistance to EGFR-targeted drugs. Results We investigated the correlation between EGFR mutations and EGFR-receptor tyrosine kinase (RTK) crosstalk in the signaling network, in order to uncover the drug resistance mechanism induced by EGFR mutations. For several EGFR wild type (WT) or mutated proteins, we measured the EGFR-RTK interactions using several computational methods based on molecular dynamics (MD) simulations, including geometrical characterization of the interfaces and conventional estimation of free energy of binding. Geometrical properties, namely the matching rate of atomic solid angles in the interfaces and center-of-mass distances between interacting atoms, were extracted relying on Alpha Shape modeling. For a couple of RTK partners (c-Met, ErbB2 and IGF-1R), results have shown a looser EGFR-RTK crosstalk for the drug-sensitive EGFR mutant while a tighter crosstalk for the drug-resistant mutant. It guarantees the genotype-determined EGFR-RTK crosstalk, and further proposes a potential drug resistance mechanism by amplified EGFR-RTK crosstalk induced by EGFR mutations. Conclusions This study will lead to a deeper understanding of EGFR mutation-induced drug resistance mechanisms and promote the design of innovative drugs.

The physical properties of agricultural products are essential in designing machines, equipment, and systems for efficient processing operations. Two periwinkle varieties, viz Tympanotonus fuscatus (Linnaeus, 1758) and Pachymelania aurita O. F. Müller, 1774, were utilised in this study to investigate and determine their physical properties relevant to the design of efficient processing equipment. The geometric (axial dimensions, mean diameters, surface area, sphericity, aspect ratio) and gravimetric (bulk and true densities, mass, and porosity) properties were measured. The averages for the major diameter, arithmetic mean diameter, geometrical mean diameter, and surface area were highest in the T. fuscatus variety. In contrast, the minor diameter, sphericity, and aspect ratio were highest in the P. aurita variety. The average bulk and true densities, porosity, and average periwinkle weight for T. fuscatus were higher than the P. aurita variety. Tukey's pairwise comparison analysis carried out on all the physical properties of the T. fuscatus, and P. aurita varieties of the periwinkle shells revealed a statistically significant difference at P < 5%.

Metal inert gas (MIG) welding is one of the processes most commonly used for joining metals, especially for joining aluminum and its alloys. The application of a pulsed current in an electric arc allows better controllability of the molten droplets and the arc transition, which subsequently leads to welds with characteristic flaky joints of better quality. In this paper, the optimization of parameters for welding aluminum alloys using the synchropulse welding process is investigated. By observing the input variables that have the greatest influence on the change in appearance of the welding current characteristics (delta wire feed from 0.1 to 6.0 m/min, frequency F from 0.5 to 3 Hz, duty cycle from 10% to 90%), it is possible to perform an optimization to achieve the desired output values. The output variables of the experiments are defined as insufficient/excessive throat thickness (mm), depth of penetration (mm), and weld width (mm); and for the desired quality of the welded joint the most acceptable range of its values is selected, the numerical optimization implementation. The experiment has shown that the delta wire feed has the greatest effect on the observed properties, while the influence of frequency F and duty cycle is somewhat smaller, but the factors responsible for the observed output properties are still significant. From all this, it is possible to select specific values of these input variables to define the best possible observed properties and to determine the characteristics of the defined mathematical models. [ABSTRACT FROM AUTHOR]

Generalized Bernstein-like functions (gB-like functions) with different shape parameters are used in this work. Parametric and geometric conditions in generalized form are developed. Some numerical examples of the parametric continuity (PC) and geometric continuity (GC) constraints of generalized Bézier-like curves (gB-like curves) are analyzed with graphical representation. Bézier-like symmetric rotation surfaces are constructed by gB-like curves. Vase and Capsule Taurus surfaces are modeled with the help of symmetry. The effect of shape parameters on surfaces are also analyzed. The illustrating figures reveal that the proposed curves and surfaces yield an accommodating strategy and mathematical depiction of Bézier curves and surfaces, allowing them to be a beneficial way to describe curves and surfaces. [ABSTRACT FROM AUTHOR]

We are concerned with free boundary problems arising from the analysis of multidimensional transonic shock waves for the Euler equations in compressible fluid dynamics. In this expository paper, we survey some recent developments in the analysis of multidimensional transonic shock waves and corresponding free boundary problems for the compressible Euler equations and related nonlinear partial differential equations (PDEs) of mixed type. The nonlinear PDEs under our analysis include the steady Euler equations for potential flow, the steady full Euler equations, the unsteady Euler equations for potential flow, and related nonlinear PDEs of mixed elliptic--hyperbolic type. The transonic shock problems include the problem of steady transonic flow past solid wedges, the von Neumann problem for shock reflection--diffraction, and the Prandtl--Meyer problem for unsteady supersonic flow onto solid wedges. We first show how these longstanding multidimensional transonic shock problems can be formulated as free boundary problems for the compressible Euler equations and related nonlinear PDEs of mixed type. Then we present an effective nonlinear method and related ideas and techniques to solve these free boundary problems. The method, ideas, and techniques should be useful to analyze other longstanding and newly emerging free boundary problems for nonlinear PDEs. [ABSTRACT FROM AUTHOR]

Epidermal growth factor receptor (EGFR) plays an important role in lung cell proliferation. Dimerization of EGFR family members and other receptor tyrosine kinases (RTKs) act as a vital controller for lung cell life cycle signals. Mutations in the kinase domain of EGFR may disorder the signaling networks and lead to cancer. Drug resistance occurs in several generations of EGFR drugs due to genetic mutations, and there is a very less understanding about the mechanism of EGFR-mutated drug resistance. In this work, we investigate the mechanism of wild type EGFR protein and its drug-sensitive and drug-resistant mutations. We performed molecular dynamics (MD) simulation for the 10-ns EGFR-drug mutant complex and investigated the structures' geometrical properties. With features extracted by alpha shape modeling, different geometrical properties, such as matching rates of atom solid angles at interaction sites and centroid distances between interfacial atoms, were calculated to characterize the binding intensity. Wilcoxon rank sum test was applied to reveal the differences between mutations based on extracted properties. We have developed a framework that explains the drug resistance mechanism based on geometrical properties and binding free energy. Results revealed that drug-sensitive mutants have tighter interactions with corresponding RTK in the complex for all protein-drug systems, while drug-resistant mutants are bound looser. The extracted geometrical properties of the drug mutant complex help understand the drug response mechanism at atomic level.

Sesame and black caraway seeds are important oil and medicinal grains that are small sized. The development of handling, processing, and storage facilities for the crops has been hampered by difficulties in measuring their geometric and gravimetric properties using Vernier caliper and micrometer screw gauge. Image analysis technique was chosen and applied in this study. Images of the seeds at different moisture levels were captured using a high resolution digital camera. The images in RGB were converted to Gray, then to Binary, and Noise was filtered, and the images subjected to threshold segmentation and analysis using LABVIEW software. Grain projected area and axial dimensions were determined. Volume was determined using liquid displacement. Dimensional analysis was used to select an appropriate grain shape as oblate spheroid. Calculated volume was obtained, and volume correction factor determined. One thousand grain mass was obtained using an electronic balance. Particle and bulk densities were determined using standard methods. Porosity was calculated using its relationship with particle and bulk densities. Results showed that as the moisture content of sesame and black caraway grains increased from 2.25% to 28.53% and 3.04% to 39.62%, respectively, the projected area, major and minor axes increased from 3.37 mm2 to 5.68 mm2, 0.3 mm to 0.452 mm and 0.287 mm to 0.45 mm (sesame), and from 1.041 mm2 to 5.136 mm2, 0.23 mm to 0.38 mm and 0.227 mm to 0.373 mm (caraway). In the above moisture ranges, volume and volume correction factor varied from 0.0214 mm3 to 0.0317 mm3 and 0.851 to 0.865 (sesame), and 0.01 mm3 to 0.0283 mm3 and 0.85 to 0.879 (caraway), respectively. W1000 increased from 2.9 to 3.875 g (sesame) and 2.644 to 3.78 g (caraway) while bulk and particle densities, and porosity decreased from 502.1 kg/m3 to 310.87 kg/m3, 828 kg/m3 to 378.4 kg/m3, and 39.4% to 17.85% for sesame, and from 560 kg/m3 to 269.8 kg/m3, 746.4 kg/m3 to 295.5 kg/m3, and 24.97% to 8.7% for caraway seed.

The objective of the study was to determine the geometric, gravimetric, aerodynamic, and frictional properties of maize grain as affected by varietal differences and moisture content. Honampa, Omankwa, Abontem, Timtim, and Obatanpa were the five maize grain varieties studied. Moisture content, geometric properties, gravimetric properties, aerodynamic properties, and frictional properties were studied. The geometric mean diameters ranged between 6.65 and 7.55 mm, while projected areas ranged between 52.98 and 73.12 m2. The surface area was between 139.69 and 180.29 mm2, and sphericity was from 0.71 to 0.80. The following ranges were obtained as thousand grain weight (213.74 and 292.89 g), and bulk density (709.50 and 746.00 kg/m3). The volume of a single seed was between 1.71 × 10−7 and 2.34 × 10−7 m3 while true density was 1250.0 kg/m3. Porosity ranged from 40.32% to 43.24% and terminal velocity ranged between 2.12 and 2.98 m/s. Drag coefficient of 7.18 to 14.60, drag force of 0.002 to 0.003, and Reynolds number between 992.71 and 1579.20 were similarly obtained. The static angle of repose varied with material surfaces while the dynamic angle of repose varied with grain variety. The grain demonstrated 19° static angle of repose, which portrays a very free flow. All the geometric properties increased with moisture besides sphericity although insignificant. The thousand grain weight, volume of single grain, and porosity increased with moisture content. Nonetheless, bulk density decreased and true density remained the same as moisture content increased. Terminal velocity, Reynolds number, and drag force increased as drag coefficient decreased with moisture content. The frictional properties increased with moisture content, and the Reynolds number was <2100, hence, the linear flow of grain. Geometric, gravimetric, aerodynamic, and frictional properties of maize grain were dependent on both grain variety and moisture content. [ABSTRACT FROM AUTHOR]

Purpose: The aim of this study was to evaluate the influence of the geometric shape on the dissolution rate of the domperidone, a drug model for immediate release dosage form. In this regard, a lack of sufficient information about the effective dissolution rate of the drugs regarding their shapes has made this issue an interesting subject for researchers. Methods: For this purpose, three tablet shapes, namely flat and biconvex both in a round and oblong shapes, with different four sizes were modelled for the preparation of domperidone tablet. In vitro dissolution test was accomplished using a USP dissolution apparatus II. The drug dissolution rate was assessed by calculating various dissolution parameters; e.g., dissolution efficiency (DE), mean dissolution rate (MDR), mean dissolution time (MDT), and difference and similarity factors (f1 and f2 ). Results: Regarding the disintegration time, the larger tablets showed a faster disintegration time. When the size of the tablets was smaller, the amount of released drug was significantly decreased. In addition, #9 tablets with a flat or biconvex geometry had obvious effects on the DE values. Generally, biconvex tablets had higher DE percentage than the flat tablets. Conclusion: Noticeable differences in dissolution parameters by considering the different geometric shapes play an important role in the drug release kinetics which makes a significant effect on quick onset of action in oral administration.

The incomplete gamma function Γ(a, u) is defined by Γ(a, u) = ∫u∞ta−1e−tdt, where u > 0. Using the incomplete gamma function, we define a new Poisson like regular matrix P(μ) = (pnkμ) given by pnkμ = n! Γ(n+1, μ) e−μμkk! (0 ≤ k ≤ n), 0 (k > n), where μ > 0 is fixed. We introduce the sequence space ℓp(P(μ)) for 1 ≤ p ≤ ∞ and some topological properties, inclusion relations and generalized duals of the newly defined space are discussed. Also we characterize certain matrix classes and compact operators related to the space ℓp(P(μ)). We obtain Gurarii's modulus of convexity and investigate some geometric properties of the new space. Finally, spectrum of the operator P(μ) on sequence space c0 has been investigated. [ABSTRACT FROM AUTHOR]

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In the present paper, an interesting subclass of meromorphic univalent functions defined on a punctured unit disk E={z:|z|1>1} has been considered and studied. A sufficient condition for these functions to be univalent and sense preserving in the class has been obtained. Certain geometric properties of the functions of the subclass of meromorphic functions has been discussed, such as coefficient inequality, starlike-ness, convexity, growth and distortion, convex linear combination and extreme points of the functions of the class by fixing some Taylor coefficients. [ABSTRACT FROM AUTHOR]

Background: Epidermal growth factor receptor (EGFR) and its signaling pathways play a vital role in pathogenesis of lung cancer. By disturbing EGFR signaling, mutations of EGFR may lead to progression of cancer or the emergence of resistance to EGFR-targeted drugs. Results: We investigated the correlation between EGFR mutations and EGFR-receptor tyrosine kinase (RTK) crosstalk in the signaling network, in order to uncover the drug resistance mechanism induced by EGFR mutations. For several EGFR wild type (WT) or mutated proteins, we measured the EGFR-RTK interactions using several computational methods based on molecular dynamics (MD) simulations, including geometrical characterization of the interfaces and conventional estimation of free energy of binding. Geometrical properties, namely the matching rate of atomic solid angles in the interfaces and center-of-mass distances between interacting atoms, were extracted relying on Alpha Shape modeling. For a couple of RTK partners (c-Met, ErbB2 and IGF-1R), results have shown a looser EGFR-RTK crosstalk for the drug-sensitive EGFR mutant while a tighter crosstalk for the drug-resistant mutant. It guarantees the genotype-determined EGFR-RTK crosstalk, and further proposes a potential drug resistance mechanism by amplified EGFR-RTK crosstalk induced by EGFR mutations. Conclusions: This study will lead to a deeper understanding of EGFR mutation-induced drug resistance mechanisms and promote the design of innovative drugs. [ABSTRACT FROM AUTHOR]