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The aim of this study is to obtain several inequalities involving the Berezin number and the Berezin norm for various combinations of operators acting on a reproducing kernel Hilbert space. First, we present some bounds regarding the Berezin number associated with W*Q+W*Q′{W}^{* }Q+{W}^{* }Q^{\prime} , where WW, QQ, and Q′Q^{\prime} are three bounded linear operators. Next, several Berezin norm and Berezin number inequalities for the sum of nn operators are established.

This study aims to describe and explain what are the types of student learning difficulties in grades 2 summation material at SDN Keboncau IV, this research uses a qualitative approach and a qualitative description research method. Subjects in this study were grade 2 students, totatling 5 students. Data collection techniques using observation, interviews and tests in the form of essays totaling 5 questions. The addition material test is used to strengthen students’ answers regarding their understanding of the addition material. It can be concluded that the dominant difficulties occur in grade 2 at SDN Keboncau IV, namely difficulties in arithmetic, difficulties in connecting concepts with existing reality, and difficulties in solving addition problems in the form of stories.

It is common knowledge that matrix equalities involving ordinary algebraic operations of inverses or generalized inverses of given matrices can be constructed arbitrarily from theoretical and applied points of view because of the noncommutativity of the matrix algebra and singularity of given matrices. Two of such matrix equality examples are given by $ A_1B_1^{g_1}C_1 + A_2B_2^{g_2}C_2 + \cdots + A_kB_k^{g_k}C_{k} = D $ and $ A_1B_1^{g_1}A_2B_2^{g_2} \cdots A_kB_k^{g_k}A_{k+1} = A $, where $ A_1 $, $ A_2 $, $ \ldots $, $ A_{k+1} $, $ C_1 $, $ C_2 $, $ \ldots $, $ C_{k} $ and $ A $ and $ D $ are given, and $ B_1^{g_1} $, $ B_2^{g_2} $, $ \ldots $, $ B_k^{g_k} $ are generalized inverses of matrices $ B_1 $, $ B_2 $, $ \ldots $, $ B_k $. These two matrix equalities include many concrete cases for different choices of the generalized inverses, and they have been attractive research topics in the area of generalized inverse theory. As an ongoing investigation of this subject, the present author presents in this article several groups of new results and facts on constructing and characterizing the above matrix equalities for the mixed combinations of $ \{1\} $- and $ \{1, 2\} $-generalized inverses of matrices with $ k = 2, 3 $ by using some elementary methods, including a series of explicit rank equalities for block matrices.

Introduction Groundwater is an important resource for domestic, agricultural, and industrial purposes (Andualem and Demeke, 2019). However, the growing population and advanced irrigation technologies have significantly led to increased groundwater exploitation resulting in aquifer depletion. Exploitation of groundwater from fractured rock aquifers using wells to supply drinking water is more sustainable than the utilization of springs with low and variable discharge. In the case of drought and periods of critical condition of water usage, springs of fractured rock aquifers may dry up or decrease making them unreliable water resources to supply drinking water. Over recent decades, the use of fractured rock and karstic units as a remarkable water resource is known as a valuable source of freshwater worldwide. However, these aquifers are extremely vulnerable to contamination due to their unique hydrogeological characteristics and require more protection (Zarvash & Vaezi, 2014). These resources contribute to providing more than 70% of the rural population and around 50% of the urban population with drinking and household demand needs. Since the degree of development of karst landforms varies substantially from region to region, exploring groundwater potential zones in karstic or fractured rock domains across the world is important, which is mostly achieved using evaluating affecting factors in creating the groundwater occurrence. This evaluation is done by incorporating weighted factors such as Weighted Overlay, Weighted Sum, and Fuzzy Overlay and utilizing geographic information systems (GIS) or other remote sensing techniques, which is addressed frequently in literature summarized by Vaezihir and Tabarmayeh (2016); Seif and Kargar (2011); and Amiri et al. (2021). Considering the importance of such issue, this research aims to investigate the potential of karstic or fractured rock resources in West Azerbaijan to gain more insight into this valuable resource of groundwater. Materials and MethodsWest Azerbaijan province, with an area of 43,660 km² including Lake Urmia, is equivalent to 2.65% of the total area of Iran and located in the Alborz-Azerbaijan structural zone with a mean annual precipitation of about 370 mm. The maximum temperature of this province, dominated by a semi-arid and Mediterranean climate, is recorded in Shahin Dezh and Miandoab, and the minimum is measured in Chaldoran, and Tekab Metrological Stations, respectively. About 78% of the total area of West Azerbaijan province is formed by karstic units with more spatial distribution in the southern area. This karstic area encompasses 71% of the total province springs with 59% of the total discharge. In the current research, lithology unit types, fracture density, elevation, slope, aspect, drainage density, and vegetation coverage, along with the precipitation, area, and humidity index as the main factors were regarded as governing factors in the development of karst aquifers, have been considered to evaluate the potential groundwater resources. After the preparation of all affected layers using various data resources including available geological maps digital elevation map of West Azerbaijan Province obtained from the Geological Survey and Mineral Exploration of Iran, Landsat satellite data, the Fuzzy logistic and SUM and Weighted overlay technique has been used to prepared groundwater potential zone. Results and DiscussionThe groundwater potential zone were determined through combining 9 affected layers in developing the groundwater resource. The results obtained based on employing both weighted overlay and SUM were classified into 5 classes including low, very low, medium, high and very high potential zones. The index value in SUM methods estimated to be 16.24, 26.24, 24.24, 20.95, 12.13%, while it changes to 22.82, 24.13, 22.14, 16.23, and 14.67 respectively. Overlaying the location of springs as an indicators of groundwater resource on hardrock and karstic domain on generated maps showed that 30.9 and 33.08 percentage of springs fall in area with the high and very high potential zone, respectively. A significant differences on maps generated based on two mentioned technique, particularly in area classified as low potential zone with 24.13 and 16.24 percent in weighted overlay and SUM. ConclusionInvestigation of the groundwater potential zone by integrating the layer provided by Fuzzy logic technique through two SUM and weighted overlay methods indicated the province of Azerbaijan Arabi has a moderate level of classification. However, in some areas, there were significantly higher or lower potentials.

It is common knowledge that matrix equalities involving ordinary algebraic operations of inverses or generalized inverses of given matrices can be constructed arbitrarily from theoretical and applied points of view because of the noncommutativity of the matrix algebra and singularity of given matrices. Two of such matrix equality examples are given by A 1 B 1 g 1 C 1 + A 2 B 2 g 2 C 2 + ⋯ + A k B k g k C k = D and A 1 B 1 g 1 A 2 B 2 g 2 ⋯ A k B k g k A k + 1 = A , where A 1 , A 2 , ... , A k + 1 , C 1 , C 2 , ... , C k and A and D are given, and B 1 g 1 , B 2 g 2 , ... , B k g k are generalized inverses of matrices B 1 , B 2 , ... , B k . These two matrix equalities include many concrete cases for different choices of the generalized inverses, and they have been attractive research topics in the area of generalized inverse theory. As an ongoing investigation of this subject, the present author presents in this article several groups of new results and facts on constructing and characterizing the above matrix equalities for the mixed combinations of { 1 } - and { 1 , 2 } -generalized inverses of matrices with k = 2 , 3 by using some elementary methods, including a series of explicit rank equalities for block matrices. [ABSTRACT FROM AUTHOR]

Our aim in this article is to establish several new norm and numerical radius inequalities for products and sums of operators acting on a complex Hilbert space (H , 〈 · , · 〉) . Some of the obtained inequalities improve well known ones. In addition, by using new techniques, we prove certain new inequalities related to ω A (·) and | | · | | A , where ω A (T) and | | T | | A denote the A-numerical radius and the A-operator seminorm of an operator T acting on the semi-Hilbert space (H , 〈 · , · 〉 A) , respectively. Here 〈 x , y 〉 A : = 〈 A x , y 〉 for every x , y ∈ H . [ABSTRACT FROM AUTHOR]

Since the finite sum of g-frames for a Hilbert space H may not be a g-frame for H, the sum of g-frames in Hilbert spaces are discussed in the present study. In fact, we first provide new sufficient conditions under which the sum of a g-frame and a g-Bessel sequence for a Hilbert space H is a g-frame for H. Subsequently, some results concerning the stability of g-frames for a Hilbert space H are obtained under some types of perturbations. [ABSTRACT FROM AUTHOR]

The purpose of this article is to explore various inequalities pertaining to the numerical radius of operators in a Hilbert space. Additionally, we present several bounds for the Berezin number and Berezin norm of operators that act on a reproducing kernel Hilbert space. Finally, we establish a necessary and sufficient condition for the triangle inequality related to the Berezin number to hold. [ABSTRACT FROM AUTHOR]

Mereological atomism is the thesis that everything is ultimately composed of atomic parts, i.e., parts without proper parts. Typically, this thesis is characterized by an axiom stating that everything has atomic parts. The present paper argues that the success of this standard characterization depends on how the notions of sum and composition are defined. In particular, we put forward a novel definition of mereological sum that: (i) is not equivalent to existing definitions in the literature, if no strong decomposition principle is assumed; (ii) can be used to argue that the standard characterization of atomism fails, because having atomic parts is not sufficient to be a sum of atoms; and (iii) provides a purely mereological distinction between structured and unstructured wholes, contributing to the ongoing debate on this crucial topic. [ABSTRACT FROM AUTHOR]

The floor and ceiling functions appear often in mathematics and manipulating sums involving floors and ceilings is a subtle game. Fortunately, the well-known textbook Concrete Mathematics provides a nice introduction with a number of techniques explained and a number of single or double sums treated as exercises. For two such double sums we provide their single-sum analogues. These closed-form identities are given in terms of a dual partition of the multiset (regarded as a partition) of all b-ary digits of a nonnegative integer. We also present the double- and single-sum analogues involving the fractional part function and the shifted fractional part function. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Al-Anbar University for Islamic Sciences is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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

With the aid of convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein's theorem for completely monotonic functions, and other analytic techniques, the author presents decreasing property of a ratio constituted via three derivatives of a sum involving trigamma function and discovers necessary and sufficient conditions for a function constituted via three derivatives of a function involving trigamma function to be completely monotonic. [ABSTRACT FROM AUTHOR]

Sums of double sine series with coefficients multiply monotone by subsequences are studied. Conditions under which these sums belong to weighted spaces are obtained. [ABSTRACT FROM AUTHOR]

The exact value of error of interval quadrature formulas $$\int_0^{2\pi}f(t)dt -\frac{\pi}{nh}\sum_{k=0}^{n-1}\int_{-h}^hf(t+\frac {2k\pi}{n})dt = R_n(f;\vec{c_0};\vec{x_0};h)$$ obtained for the classes $W^rH^{\omega} (r=1,2,...)$ of differentiable periodic functions for which the modulus of continuity of the $r -$th derivative is majorized by the given modulus of continuity $\omega(t)$. This interval quadrature formula coincides with the rectangles formula for the Steklov functions $f_h(t)$ and is optimal for some important classes of functions.

Considering that there can be many developments in VLSI innovation and there are masses of reliable varieties of growing VLSI circuits. A few of the styles are CMOS, PTL, GDI (Gate Diffusion Input) strategies. GDI method lets in making low-electricity digital combinatorial circuit with the aid of which we're able to remove terrible marks of CMOS, PTL strategies. This approach permits reducing electricity intake, breeding maintain-up, in addition to location of virtual circuits even as retaining low intricacy of reasoning format. This paper goes over regarding the performance characteristics of a Full Adder primarily based definitely Carry Select Adder making use of numerous logics in addition to furthermore GDI-MUX method. The adders are applied in hundreds of information path packages in addition to moreover the area, power utilization and maintain-up in the style can be reduced. The proposed method is the GDI-Mix which lets in the decrease of above talked about requirements further to likewise lower the kind of transistors. The Full Adder based totally Carry Select Adder made in Complementary Pass Transistor Logic, Complementary Metal Oxide Semiconductor Reasoning and moreover Gateway Diffusion Input-- Mix and they are contrasted and additionally the greenest technique is diagnosed. The numerous strategies are in assessment to treat to the format location; transistor be counted range, hold-up, and furthermore power dissipation are prolonged long past over proper right here on this paper showing benefits and drawbacks of GDI contrasted to CMOS layout [ABSTRACT FROM AUTHOR]

Sum and intersection of linear subspaces in a vector space over a field are fundamental operations in linear algebra. The purpose of this survey paper is to give a comprehensive approach to the sums and intersections of two linear subspaces and their orthogonal complements in the finite-dimensional complex vector space. We shall establish a variety of closed-form formulas for representing the direct sum decompositions of the m-dimensional complex column vector space 𝔺m with respect to a pair of given linear subspaces 𝒨 and 𝒩 and their operations, and use them to derive a huge amount of decomposition identities for matrix expressions composed by a pair of orthogonal projectors onto the linear subspaces. As applications, we give matrix representation for the orthogonal projectors onto the intersections of a pair of linear subspaces using various matrix decomposition identities and Moore–Penrose inverses; necessary and su˚cient conditions for two linear subspaces to be in generic position; characterization of the commutativity of a pair of orthogonal projectors; necessary and su˚cient conditions for equalities and inequalities for a pair of subspaces to hold; equalities and inequalities for norms of a pair of orthogonal projectors and their operations; as well as a collection of characterizations of EP-matrix.

The article considers the temperature distribution in steel at its continuous teeming. The temperatures were measured sequentially in the steel-teeming ladle (one measurement) and the tundish (two measurements) using a platinum-platinum-rhodium thermocouple with an accuracy of ±4°C. This work analyzes the results of 170 casts of grade 5SP and 35GS steels. The type of temperature set distribution was checked against three goodness-of-fit criteria: Pearson χ-square test, Kolmogorov–Smirnov test λ and Shapiro–Wilk test W. It is shown that the temperatures in the steel-teeming ladle for various kinds of steel fit within the normal distribution model. The results obtained are consistent with the physics of steel casting. The metal in the steel-teeming ladle is practically stable and subject only to natural cooling through the lining, top and body of the ladle. However, in case of analyzing a sample of temperatures in the tundish at the first and second measurement, the normal distribution hypothesis should be rejected. Here, the steel temperature depends on a number of parameters, including the feed rate, casting rate, feed time, composition of slag-forming and heat-insulating mixtures, and others. The attempts to establish the relationship between the steel temperatures in the steel-teeming ladle and in the tundish were unsuccessful. Considering the temperature measurements in the tundish as two sequential data arrays, the first of which is an argument, and the second is a function, a linear relationship between the arrays is established. This relationship can be used to estimate the final steel temperature at the dropout of thermocouple readings, including in the event of a failure. The results of the work can be used in developing a mathematical model of steel teeming. [ABSTRACT FROM AUTHOR]

The purpose of this study is to extend the Fermatean fuzzy matrices to the theory of Hamacher operations. In this paper, the concept of Hamacher operations of Fermatean fuzzy matrices are introduced and some desirable properties of these operations, such as commutativity, idempotency, and monotonicity are discussed. Further, we prove DeMorgan’s laws over complement for these operations. Furthermore, the scalar multiplication and exponentiation operations of Fermatean fuzzy matrices are constructed and their algebraic properties are investigated. Finally, some properties of necessity and possibility operators of Fermatean fuzzy matrices are proved. [ABSTRACT FROM AUTHOR]

We study a countably infinite iteration of the natural product between ordinals.We present an “effective” way to compute this countable natural product; in the non trivial cases the result depends only on the natural sum of the degrees of the factors, where the degree of a nonzero ordinal is the largest exponent in its Cantor normal form representation. Thus we are able to lift former results about infinitary sums to infinitary products. Finally, we provide an order-theoretical characterization of the infinite natural product; this characterization merges in a nontrivial way a theorem by Carruth describing the natural product of two ordinals and a known description of the ordinal product of a possibly infinite sequence of ordinals.

In the paper, the authors find the sum of the Lah numbers and make sure that the Kummer confluent hypergeometric function 1F1(n+ 1; 2; z) has only n− 1real and negative zeros.

Several studies suggest that neurons from the lateral region of the SuM (SuML) innervating the dorsal dentate gyrus (DG) display a dual GABAergic and glutamatergic transmission and are specifically activated during paradoxical (REM) sleep (PS). The objective of the present study is to characterize the anatomical, neurochemical and electrophysiological properties of the SuML-DG projection neurons and to determine how they control DG oscillations and neuronal activation during PS and other vigilance states. For this purpose, we combine structural connectivity techniques using neurotropic viral vectors (rabies virus, AAV), neurochemical anatomy (immunohistochemistry, in situ hybridization) and imaging (light, electron and confocal microscopy) with in vitro (patch clamp) and in vivo (LFP, EEG) optogenetic and electrophysiological recordings performed in transgenic VGLUT2-cre male mice. At the cellular level, we show that the SuML-DG neurons co-release GABA and glutamate on dentate granule cells and increase the activity of a subset of DG granule cells. At the network level, we show that activation of the SuML-DG pathway increases theta power and frequency during PS as well as gamma power during PS and waking in the DG. At the behavioral level, we show that the activation of this pathway does not change animal behavior during PS, induces awakening during slow wave sleep and increases motor activity during waking. These results suggest that the SuML-DG pathway is capable of supporting the increase of theta and gamma power in the DG observed during PS and plays an important modulatory role of DG network activity during this state. [ABSTRACT FROM AUTHOR]

Sums of double sine and cosine series with multiply monotone coefficients are studied. Sufficient conditions for such sums to belong to Orlich's weighted classes are obtained. [ABSTRACT FROM AUTHOR]

Some Gaussian q-binomial sum identities from [3] are further generalized, introducing two additional parameters. We prove the claimed results by q-calculus. Finally we present applications to the generalized Fibonomial sums as corollaries. [ABSTRACT FROM AUTHOR]

In recent years, research on a special class of frames, named K-frames where K is an operator, has become significant in theory and applications. Since the finite sum of K-frames may not be a K-frame for the Hilbert space, in this paper, we discuss the sum and stability of K-frames in Hilbert spaces. First, we obtain some sufficient conditions for the finite sum of a K-frame and a Bessel sequence to be a K-frame. Then we get the K-dual of the sum of K-frames by the dual of the original K-frames. In particular, we give some new results about the operator K and the analysis operator in the discussion. Moreover, we discuss the stability of K-frames and get some conclusions. [ABSTRACT FROM AUTHOR]

In Dedekind-finite ring, we present the group inverse of sum of two group invertible elements under different conditions. Then, the core inverse of a sum of two core invertible elements is investigated. Furthermore, the core inverse of the difference of two core invertible elements is presented. These results generalized the corresponding results of complex matrices. [ABSTRACT FROM AUTHOR]

در سال‌های اخیر با پیشرفت فن‌آوری‌های جمع‌آوری و مدیریت‌داده، پایگاه‌داده‌های بسیار بزرگ پدیدار شده‌اند. بسیاری از پرس‌وجوهای تجزیه‌ و تحلیل بر اساس ماهیتشان به تجمیع و خلاصه‌سازی بخش‌­های بزرگی از داده­‌های در حال تجزیه ‌و تحلیل نیاز دارند. مسئله اصلی در حیطه‌ی پایگاه داده پردازش کارآمد پرس‌وجو مخصوصاً در سیستم‌های لحظه‌ای[1] است که نیازمند رسیدن به جواب آنی می‌باشد تا اینکه کاربر زمان زیادی را برای دریافت پاسخ صرف نکند. (AQP (Approximate Query Processingبه‌عنوان روشی جایگزین برای پردازش پرس‌وجو‌ در محیط‌هایی که ارائه یک پاسخ دقیق زمان‌بر است، با هدف ارائه پاسخ تخمینی، کاهش زمان پاسخ را با حذف یا کاهش تعداد دسترسی‌ها به داده‌ی پایه میسر می‌سازد. پردازش [2]In-Database عملکرد شبکه‌های کامپیوتری را بهبود بخشیده و به طراحی مناسب پرس‌وجو‌ها با نتایج نسبتاً سریع و دقیق کمک می‌کند. در این پژوهش عملیات تجمیع (Sum) در پایگاه داده PostgreSQL روی داده‌های رستری بارش به دو روش معمولی و بهینه پیشنهاد شده، انجام شده است. بررسی نتایج نشان می‌دهد که سرعت اجرای تابع Sum با خوشه‌بندی، 2/27 برابر اجرای این تابع بدون خوشه‌بندی است و میانگین اختلاف عددی پیکسل‌های حاصل از اجرای تابع Sum بهینه با اجرای تابع معمولی آن 028/0 می‌باشد.میانگین زمان اجرای پرس‌وجوهای معمولی و بهینه برای تابع Sum به ترتیب 211 و 754/7 ثانیه می‌باشد که نشانگر کارآمد بودن روش پیشنهاد شده در این تحقیق می‌باشد. نتایج تحقیق حاضر که در حقیقت کاهش معنی دار زمان پاسخ آنالیزهای داخل پایگاه داده‌ای در داده‌های رستری می‌باشد، می‌تواند در ارائه سرویس‌های رئال تایم تحت وب مانند هواشناسی، ترافیک و ... که نیازمند تحلیل‌های آنی و جواب لحظه‌ای می‌باشند مورد استفاده قرار گیرد. [1]- Real time [2]- درون پایگاه‌داده