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This study introduces a technique for determining surface orientations by projecting a monochrome, spatial pixel-encoded pattern and calculating the surface normals from single-shot measurement. Our method differs from traditional methods, such as shape from shading and shape from texture, in that it does not require relating the local surface orientations of adjacent points. We propose a multi-resolution system incorporating symbols varying in sizes from 8 × 8, 10 × 10, 12 × 12, 14 × 14, and 16 × 16 pixels. Compared to previous methods, we have achieved a denser reconstruction and obtained a 5.2 mm resolution using an 8 × 8 pattern at a depth of 110 cm. Unlike previous methods, which used local point orientations of grid intersection and multiple colors, we have used the monochrome pattern and deterministic centroid positions to compute the unit vector or direction vector between the neighboring symbols. The light plane intersections are used to calculate the tangent vectors on the surface. Surface normals are determined by the cross-product of two tangent vectors on the surface. A real experiment was conducted to measure simple plane surfaces, circular surfaces, and complex sculptures. The results show that the process of calculating surface normals is fast and reliable, and we have computed 1654 surface normals in 29.4 milliseconds for complex surfaces such as sculptures.

Monkeypox is a DNA virus that belongs to the family of smallpox, with an incubation period of seven to 14 days and may last up to 21 days1. The Virus replicates on reaching the host cells, from where it spreads to lymph nodes and then to distant organs. The symptoms include fever, lymphadenopathy, and mucocutaneous lesions. The infection does not spread during the incubation period but may spread on being symptomatic to drying of scabs. Smallpox vaccination protects against monkeypox but its vaccination has been developed. An outbreak of pox appeared and spread rapidly across Europe, America, and then to all six continents2.

Research for the development of noble metal-free electrodes for hydrogen evolution has blossomed in recent years. Transition metal carbides compounds, such as W2C, have been considered as a promising alternative to replace Pt-family metals as electrocatalysts towards hydrogen evolution reaction (HER). Moreover, hybridization of TMCs with graphene nanostructures has emerged as a reliable strategy for the preparation of compounds with high surface to volume ratio and abundant active sites. The present study focuses in the preparation of tungsten carbide/oxide compounds deposited in a three-dimensional vertical graphene nanowalls (VGNW) substrate via chemical vapor deposition, magnetron sputtering and thermal annealing processes. Structural and chemical characterization reveals the partial carburization and oxidation of the W film sputtered on the VGNWs, due to C and O migration from VGNWs towards W during the high temperature annealing process. Electrochemical characterization shows the enhanced performance of the nanostructured hybrid W2C/WOx on VGNW compound towards HER, when compared with planar W2C/WOx films. The W2C/WOx nanoparticles on VGNWs require an overpotential of −252 mV for the generation of 10 mA cm−2. Chronoamperometry tests in high overpotentials reveal the compounds stability while sustaining high currents, in the order of hundreds of mA. Post-chronoamperometry test XPS characterization unveils the formation of a W hydroxide layer which favours hydrogen evolution in acidic electrolytes. We aspire that the presented insights can be valuable for those working on the preparation of hybrid electrodes for electrochemical processes.

In this paper, we study a sufficient condition for subelliptic estimates in the weak $ \operatorname{Z}(k) $ domain with $ \operatorname{\operatorname{C}}^{3} $ boundary in an $ n $-dimentionsl $ \operatorname{Stein\, manifold} $ $ \operatorname{X} $. Consequently, the compactness of the $ \overline\partial $-Neumann operator $ \operatorname{N} $ on $ { M } $ is obtained and the closedness ranges of $ \overline\partial $ and $ \overline\partial^* $ are presented. The $ \operatorname{L}^2 $-setting and the Sobolev estimates of $ \operatorname{N} $ on $ { M } $ are proved. We study the $ \overline\partial $ problem with support conditions in $ { M } $ for $ \Xi $-valued $ (\operatorname{p}, \operatorname{k}) $ forms, where $ \Xi $ is the $ m $-times tensor product of holomorphic line bundle $ \Xi^{\otimes \operatorname{m}} $ for positive integer $ m $. Moreover, the compactness of the weighted $ \overline\partial $-Neumann operator is studied on an annular domain in a $ \operatorname{Stein\, manifold} $ $ { M } = { M }_{1}\backslash\overline{ M }_{2} $, between two smooth bounded domains $ { M }_{1} $ and $ { M }_{2} $ satisfy $ \overline{ M }_{2}\Subset{ M }_{1} $, $ { M }_{1} $ is weak $ Z(k) $, $ { M }_{2} $ is weak $ Z(n-1-k) $, $ 1 \leqslant k\leqslant n -2 $ with $ n \geqslant 3 $. In all cases, the closedness of $ \overline\partial $ and $ \overline\partial^* $, global boundary regularity for $ \overline\partial $ and $ \overline\partial_b $ are studied.

The aim of this paper is to present the bounds of $ k $-fractional integrals containing the Mittag-Leffler function. For establishing these bounds, a generalized convexity namely strongly exponentially $ (\alpha, h-m)-p $-convexity is utilized. The results of this article provide many new fractional inequalities for several types of fractional integrals and various kinds of convexities. Moreover, an identity is established which helps in proving a Hadamard type inequality.

This research article aims to study quotient MA-semirings determined by the prime ideals. Derivations are important tools to study algebraic structures. We establish some theorems on commutativity of quotient MA-semirings under certain differential identities. Results of this paper are extensions of many well known facts of this topic.

This paper investigates some well-known inequalities for $ q $-$ h $-integrals. These include Hölder, Ostrowski, Grüss and Opial type inequalities. Refinement of the Hadamard inequality for $ q $-$ h $-integrals is also established by applying the definition of strongly convex functions. From main theorems, $ q $-Hölder, $ q $-Ostrowski and $ q $-Grüss inequalities can be obtained in particular cases.

In the world of advanced energy conversion and storage, silicon nanostructures have garnered immense interest of scientists and innovators alike with their unique structural, electrical, optical and electrochemical properties, setting the stage for a brighter, more sustainable future. Amidst the array of top-down methods, one method stands out as an approach-change: Metal-assisted chemical etching (MacEtch). It is highlighted for its cost-effectiveness, simplicity, versatility and scalability, making it a crucial point in the world of micro/nano Si structure fabrication. Recent breakthroughs have propelled MacEtch into the limelight, making it the go-to technique for crafting micro/nano structures with exceptional electrochemical attributes. These structures are tailor-made for energy storage applications, from lithium-ion batteries (LIBs) to supercapacitors. Join us in this captivating feature article as we unveil the mechanism underlying the MacEtch’s silicon transformation. Explore the latest and old strides achieved in the field of Silicon nanowires (SiNWs) generated through MacEtch, particularly in the context of their electrochemical properties for energy storage applications.

This paper aims to find generalizations of inequalities that hold for unified integral operators by applying strongly exponentially α,ℏ−m−p-convex functions. These inequalities generate results for several fractional integral operators and simultaneously hold for convex, strongly convex, and exponentially convex functions. The particular cases of presented inequalities are directly connected with many recently published results.

The well-known Hermite-Hadamard inequality for convex functions is extensively studied for different kinds of integrals and derivatives. This paper investigates some of its variants for $ q-h $-integrals using properties of convex functions. Inequalities for $ q $-integrals that have been published in recent years can be extracted from the main results of this paper.

This paper aims to unify q-derivative/q-integrals and h-derivative/h-integrals into a single definition, called q−h-derivative/q−h-integral. These notions are further extended on the finite interval [a,b] in the form of left and right q−h-derivatives and q−h-integrals. Some inequalities for q−h-integrals are studied and directly connected with well known results in diverse fields of science and engineering. The theory based on q-derivatives/q-integrals and h-derivatives/h-integrals can be unified using the q−h-derivative/q−h-integral concept.

In this article, a new generalized iterative technique is presented for finding the approximate solution of a system of linear equations Ax=b. The efficiency of iterative technique is analyzed by implementing it on some examples, and then comparing with existing methods. A parameter introduced in the method plays very vital role for a better and rapid solution. Convergence analysis is also examined. Findings of this paper may stimulate further research in this area.

In this paper, we define refined (α,h−m)-convex function with respect to a strictly monotone function. This function provides refinements of various well-known classes of functions for specific strictly monotone functions. By applying definition of this new function we prove the Hadamard inequalities for Riemann-Liouville fractional integrals. These inequalities give the refinements of fractional Hadamard inequalities for convex, (α,m)-convex, (h−m)-convex, (s,m)-convex, h-convex and many other related well-known classes of functions implicitly. Also, Hadamard type inequalities for k-fractional integrals are given.

For generalizations of concepts of different fields fractional derivative operators as well as fractional integral operators are useful notions. Our aim in this paper is to discuss boundedness of the integral operators which contain Mittag-Leffler function in their kernels. The results are obtained for strongly (α,h−m)-convex functions which hold for different kinds of convex functions at the same time. They also give improvements/refinements of many already published results.

This paper aims to derive fractional Grüss type integral inequalities for generalized k-fractional integral operators with Mittag-Leffler function in the kernel. Many new results can be deduced for several integral operators by giving specific values to the parameters involved in Mittag-Leffler function. Moreover, the results of this paper reproduce a lot of already published results.

In the literature of mathematical inequalities, one can have different variants of the well-known Hadamard inequality for CFD (Caputo fractional derivatives). These variants include generalizations, extensions and refinements which have been proved by defining new classes of functions. This paper aims to formulate inequalities of the Hadamard type which will simultaneously produce refinements and generalizations of many fractional versions of such inequalities that already exist in the literature. The error bounds of some existing inequalities are also proved by applying well-known identities. The results given in this paper are improvements of several well-known Hadamard type Caputo fractional derivative inequalities.

In this paper, k-fractional integral operators containing further extension of Mittag-Leffler function are defined firstly. Then, the first and second version of Hadamard and Fejér-Hadamard inequalities for generalized k-fractional integrals are obtained. Finally, by using these generalized k-fractional integrals containing Mittag-Leffler functions, results for p-convex functions are obtained. The results for convex functions can be deduced by taking p=1.

Firstly, we obtain some inequalities of Hadamard type for exponentially (θ,h−m)–convex functions via Caputo k–fractional derivatives. Secondly, using integral identity including the (n+1)–order derivative of a given function via Caputo k-fractional derivatives we prove some of its related results. Some new results are given and known results are recaptured as special cases from our results.

In this article, the bounds of unified integral operators are studied by using a new notion called refined (α,h−m)−p-convex function. The upper and lower bounds in the form of Hadamard inequality are established. From the results of this paper, refinements of well-known inequalities can be obtained by imposing additional conditions.

This article aims to investigate unified versions of the well-known Hermite–Hadamard inequality by considering q-h-integrals and properties of convex functions. Currently published results for q-integrals can be deduced from inequalities of this paper. Moreover, some new results are presented in terms of corollaries.

The aim of this article is to present fractional versions of the Hadamard type inequalities for exponentially $(s, m)$-convex functions via $k$-analogue of Riemann-Liouville fractional integrals. The results provide generalizations of various known fractional integral inequalities. Some special cases are analyzed in the form of corollaries and remarks.

This article investigates inequalities for certain types of strongly convex functions by applying q-h-integrals. These inequalities provide the refinements of some well-known results that hold for (α,m)- and (ℏ-m)-convex and related functions. Inequalities for q-integrals are deducible by vanishing the parameter h. Some particular cases are discussed after proving the main results.

In recent years, vertical graphene nanowalls (VGNWs) have gained significant attention due to their exceptional properties, including their high specific surface area, excellent electrical conductivity, scalability, and compatibility with transition metal compounds. These attributes position VGNWs as a compelling choice for various applications, such as energy storage, catalysis, and sensing, driving interest in their integration into next-generation commercial graphene-based devices. Among the diverse graphene synthesis methods, plasma-enhanced chemical vapor deposition (PECVD) stands out for its ability to create large-scale graphene films and VGNWs on diverse substrates. However, despite progress in optimizing the growth conditions to achieve micrometer-sized graphene nanowalls, a comprehensive understanding of the underlying physicochemical mechanisms that govern nanostructure formation remains elusive. Specifically, a deeper exploration of nanometric-level phenomena like nucleation, carbon precursor adsorption, and adatom surface diffusion is crucial for gaining precise control over the growth process. Hydrogen’s dual role as a co-catalyst and etchant in VGNW growth requires further investigation. This review aims to fill the knowledge gaps by investigating VGNW nucleation and growth using PECVD, with a focus on the impact of the temperature on the growth ratio and nucleation density across a broad temperature range. By providing insights into the PECVD process, this review aims to optimize the growth conditions for tailoring VGNW properties, facilitating applications in the fields of energy storage, catalysis, and sensing.

This paper aims to study the bounds of k-integral operators with the Mittag-Leffler kernel in a unified form. To achieve these bounds, the definition of exponentially (α,h−m)−p-convexity is utilized frequently. In addition, a fractional Hadamard type inequality which shows the upper and lower bounds of k-integral operators simultaneously is presented. The results are directly linked with the results of many published articles.

This article aims to obtain inequalities containing the unified Mittag–Leffler function which give bounds of integral operators for a generalized convexity. These findings provide generalizations and refinements of many inequalities. By setting values of monotone functions, it is possible to reproduce results for classical convexities. The Hadamard-type inequalities for several classes related to convex functions are identified in remarks, and some of them are also presented in last section.

Abstract This article investigates new inequalities for generalized Riemann–Liouville fractional integrals via the refined ( α , h − m ) $(\alpha ,h-m)$ -convex function. The established results give refinements of fractional integral inequalities for ( h − m ) $(h-m)$ -convex, ( α , m ) $(\alpha ,m)$ -convex, ( s , m ) $(s,m)$ -convex, and related functions. Also, the k-fractional versions of given inequalities by using a parameter substitution are provided.

In this paper Hadamard type inequalities for strongly (α,m)-convex functions via generalized Riemann-Liouville fractional integrals are studied. These inequalities provide generalizations as well as refinements of several well known inequalities. The established results are further connected with fractional integral inequalities for Riemann-Liouville fractional integrals of convex, strongly convex and strongly m-convex functions. By using two fractional integral identities some more Hadamard type inequalities are proved.

Abstract Some new integral inequalities for strongly ( α , h − m ) $(\alpha ,h-m)$ -convex functions via generalized Riemann–Liouville fractional integrals are established. The outcomes of this paper provide refinements of some fractional integral inequalities for strongly convex, strongly m-convex, strongly ( α , m ) $(\alpha ,m)$ -convex, and strongly ( h − m ) $(h-m)$ -convex functions. Also, the refinements of error estimations of these inequalities are obtained by using two fractional integral identities. Moreover, using a parameter substitution and a constant multiplier, k-fractional versions of established inequalities are also given.

In this paper we give Hadamard inequalities for exponentially (α,h−m)-convex functions using Riemann-Liouville fractional integrals for strictly increasing function. Results for Riemann-Liouville fractional integrals of convex, m-convex, s-convex, (α,m)-convex, (s,m)-convex, (h−m)-convex, (α,h−m)-convex, exponentially convex, exponentially m-convex, exponentially s-convex, exponentially (s,m)-convex, exponentially (h−m)-convex, exponentially (α,h−m)-convex functions are particular cases of the results of this paper. The error estimations of these inequalities by using two fractional integral identities are also given.

Recently, a generalization of convex function called exponentially (α,h−m)-convex function has been introduced. This generalization of convexity is used to obtain upper bounds of fractional integral operators involving Mittag-Leffler (ML) functions. Moreover, the upper bounds of left and right integrals lead to their boundedness and continuity. A modulus inequality is established for differentiable functions. The Hadamard type inequality is proved which shows upper and lower bounds of sum of left and right sided fractional integral operators.

In this article some salient characteristics of Jordan ideals of MA-semirings are discussed. We prove some results for derivations of MA-semirings satisfying different identities on their Jordan ideals and investigate commuting conditions through these ideals.

In this paper we study the Fejér-Hadamard inequalities for convex function with respect to a strictly monotone function. We establish two inequalities for convex function with respect to a strictly monotone function via Riemann-Liouville fractional integrals. From inequalities found here many new results can be derived by selecting specific strictly monotone and weight functions. Also a variety of existing Fejér-Hadamard and Hadamard inequalities can be reproduced.

This paper aims to establish generalized fractional integral inequalities for operators containing Mittag–Leffler functions. By applying (α,h−m)−p-convexity of real valued functions, generalizations of many well-known inequalities are obtained. Hadamard-type inequalities for various classes of functions are given in particular cases.

In this paper, we discuss some differential identities of MA-semirings with involution. The aim to study these identities is to induce commutativity in MA-semirings.

Abstract In this paper we are presenting the refinements of integral inequalities established for convex functions. Consequently, we get refinements of several fractional integral inequalities for different kinds of fractional integral operators.

Objective: To find out the pattern of foreign bodies inhaled or ingested in a series of patients. Study Design: Case series. Place and Duration of Study: Ear, Nose and Throat (ENT) department, Pak Emirates Military Hospital (PEMH) Rawalpindi, Jan 2016 to Dec 2016. Methodology: A total of 46 cases of foreign body upper aero digestive tract who presented in the ENT Department, PEMH Rawalpindi in 2016 were included in this study. Twenty eight cases were of foreign body esophagus and 18 were of foreign body airway. The age, gender, duration of foreign body lodgment, types of foreign body’s physical signs and symptoms were recorded. Relevant radiographic studies were performed. Results: Out of 46 patients of foreign body aero digestive tract 33 were males and 13 were females. The overall frequency of foreign bodies’ upper aero digestive tract was 46 (0.14%) with 28 (0.08%) being foreign bodies esophagus and 18 (0.06%) foreign bodies airway. In 50% cases of bronchial foreign bodies were in age group 0-3 years. The most frequent foreign body in the esophagus was coin in 13(46.4%) followed by chicken bone 5 (17.8%) and fish bone 3 (10.7%). Peanuts, peas, and beans were predominant component of the airway foreign bodies constituting 6 (33.3%), 3 (16.6%) and 3 (16.6%) respective of the total. Most frequent sites of impaction of the foreign body were cervical esophagus 16 (34%), right main bronchus 11 (23.9%) and left main bronchus 3 (6.5%). Conclusion: Foreign body aero digestive tract is an uncommon but potentially life threatening presentation in ENT practice. Prompt management includes high index of suspicion and investigation to reach definitive diagnosis followed by intervention.

Fractional calculus operators are very useful in basic sciences and engineering. In this paper we study an integral operator which is directly related with many known fractional integral operators. A new generalized convexity namely exponentially (α, h−m)-convexity is defined which has been applied to obtain the bounds of unified integral operators. A generalized Hadamard inequality is established for the generalized convex functions. The established theorems reproduce several known results.

Energy generation through wind and solar is increasing with the rising interest in the renewable and clean form of energy. Due to energy crises, the world is shifting from nonrenewable energy resources to renewable energy resources. Renewable energy resources are the green and eco-friendly sources and do not affect the climate like the other fossil fuels. Renewable fuels gain popularity due to their sustainability and low carbon emission. To get energy from renewable energy sources, well-defined mechanisms and control devices must be needed. Therefore, the reliability and stability of the system are required. The inverter is one of the tools which have a significant contribution to controlling the operation of the energy conversion system. The inverter is an accessory that changes a Direct Current (DC) source into an Alternative (AC) source. By using that AC source, we can easily derive AC appliances and drive the loads. To gain more power or to derive large power motors whose power ratings are up to several kilo/Megawatts, we need multi-level inverters. One of the types of multi-level inverters is the Neutral Point Clamped inverter (NPC). NPC inverters are used where considerable power is required, such as of several megawatts. The main contribution of this research paper is to design the three levels of neutral point clamped inverters by using the Pulse width Modulation (PWM) and Space Vector Modulation (SVM) Techniques.

The main objective of this paper is to compute refinements of bounds of the generalized fractional integral operators containing an extended generalized Mittag-Leffler function in their kernels. The presented results also provide refinements of already known bounds of different fractional integral operators for convex, m-convex, s-convex and (s, m)-convex functions. Moreover, the refinements of some known fractional versions of the Hadamard inequality are given.

Abstract This paper studies fractional integral inequalities for fractional integral operators containing extended Mittag-Leffler (ML) functions. These inequalities provide upper bounds of left- and right-sided fractional integrals for ( α , h − m ) $(\alpha, h-m)$ convex functions. A generalized fractional Hadamard inequality is established. All the results hold for h-convex, ( h , m ) $(h, m)$ -convex, ( α , m ) $(\alpha, m)$ -convex, ( s , m ) $(s, m)$ -convex, and associated functions.

Abstract The aim of this paper is to generalize the fractional Hadamard and Fejér–Hadamard inequalities. By using a generalized fractional integral operator containing extended Mittag-Leffler function via monotone function, for convex functions we generalize well known fractional Hadamard and Fejér–Hadamard inequalities. Also we study the error bounds of these generalized Hadamard and Fejér–Hadamard inequalities. We also obtain some published results from presented inequalities.

In this study, we introduce a new general identity for n th order differentiable functions. Also, we establish some new inequalities regarding general perturbed trapezoid inequality for the functions whose the absolute values of n th derivatives are convex. Finally, some applications for special means are provided.

Abstract The aim of this paper is to establish new generalized fractional versions of the Hadamard and the Fejér–Hadamard integral inequalities for harmonically convex functions. Fractional integral operators involving an extended generalized Mittag-Leffler function which are further generalized via a monotone increasing function are utilized to get these generalized fractional versions. The results of this paper give several consequent fractional inequalities for harmonically convex functions for known fractional integral operators deducible from utilized generalized fractional integral operators.

In this paper, we establish generalized fractional versions of Hermite-Hadamard inequalities for exponentially (α, h − m)-convex functions, exponentially (h − m)-convex functions and exponentially (α, m)-convex functions. These inequalities arise when using the generalized fractional integral operators containing Mittag-Leffler function via a monotonically increasing function. The presented results hold at the same time for various kinds of convexities and well-known fractional integral operators. Moreover, the established inequalities reproduce several known results which are part of the existing literature.

This paper investigates the bounds of an integral operator for several kinds of convex functions. By applying definition of (h - m)-convex function upper bounds of left sided (1.12) and right sided (1.13) integral operators are formulated which particularly provide upper bounds of various known conformable and fractional integrals. Further a modulus inequality is investigated for differentiable functions whose derivative in absolute value are (h - m)-convex. Moreover a generalized Hadamard inequality for (h - m)-convex functions is proved by utilizing these operators. Also all the results are obtained for (α, m)-convex functions. Finally some applications of proved results are discussed.

Abstract Integral operators have a very vital role in diverse fields of science and engineering. In this paper, we use φ-convex functions for unified integral operators to obtain their upper bounds and upper and lower bounds for symmetric φ-convex functions in the form of a Hadamard inequality. Also, for φ-convex functions, we obtain bounds of different known fractional and conformable fractional integrals. The results of this paper are applicable to convex functions.

Convex functions play a vital role in the derivation of inequalities. In this paper these functions are used to obtain certain bounds of a unified integral operator. A Hadamard inequality for these operators is established. Further bounds of several kinds of fractional and conformable integral operators are deduced in particular.

Abstract This research investigates the bounds of fractional integral operators containing an extended generalized Mittag-Leffler function as a kernel via several kinds of convexity. In particular, the established bounds are studied for convex functions and further connected with known results. Furthermore, these results applied to the parabolic function and consequently recurrence relations for Mittag-Leffler functions are obtained. Moreover, some fractional differential equations containing Mittag-Leffler functions are constructed and their solutions are provided by Laplace transform technique.

Abstract In this paper we have derived the fractional integral inequalities by defining exponentially ( s , m ) $(s,m)$ -convex functions. These inequalities provide upper bounds, boundedness, continuity, and Hadamard type inequality for fractional integrals containing an extended Mittag-Leffler function. The results about fractional integral operators for s-convex, m-convex, ( s , m ) $(s,m)$ -convex, exponentially convex, exponentially s-convex, and convex functions are direct consequences of presented results.

Abstract The objective of this paper is to derive the bounds of fractional and conformable integral operators for (s,m) $(s,m)$-convex functions in a unified form. Further, the upper and lower bounds of these operators are obtained in the form of a Hadamard inequality, and their various fractional versions are presented. Some connections with already known results are obtained.