Quotient Formula Research Articles

Relationship between Lesion Parameters after Radiofrequency Catheter Ablation in Striated Muscles and Parenchymal Tissue.

Background and Objectives: Radiofrequency catheter ablation (RFCA) is a highly successful intervention. By comparing the lesion changes in prostate parenchymal and striated muscle tissues after RFCA with and without cooling, it was possible to assess the correlation between the shape regularity, area, and perimeter of the thermal lesion, and to predict the geometric shape changes of the lesions. Materials and Methods: A standard prostate and striated muscle RFCA procedure was performed on 13 non-purebred dogs in two sessions: no cooling and cooling with 0.1% NaCl solution. Microtome-cut 2-3 µm sections of tissue samples were stained with haematoxylin and eosin and further examined. The quotient formula was employed to evaluate the geometric shape of the damage zones at the ablation site. Results: The extent of injury following RFCA in striated muscle tissue was comparable to that in prostate parenchymal tissue. Regression analysis indicated a strong and positive relationship between area and perimeter in all experimental groups. In the experimental groups of parenchymal tissues with and without cooling, an increase in the area or perimeter of the damage zone corresponded to an increase in the quotient value. A similar tendency was observed in the striated muscle group with cooling. However, in the striated muscle group without cooling, an increase in lesion area or perimeter lowered the quotient value. Standardised regression coefficients demonstrated that in the striated muscle with cooling, the damage zone shape was more determined by area than perimeter. However, in the parenchymal tissue, the perimeter had a more substantial impact on the damage zone shape than the area. Conclusions: The damage area and perimeter have predictive power on the overall shape regularity of damage zone geometry in both striated muscles and parenchymal tissue. This approach is employed to achieve a balance between the need for tumour eradication and the minimisation of ablation-induced complications to healthy tissue.

On the design of non-singular, energy-momentum consistent integrators for nonlinear dynamics using energy splitting and perturbation techniques

This work proposes a suite of numerical techniques to facilitate the design of structure-preserving integrators for nonlinear dynamics, with particular emphasis on many-body dynamics. The celebrated LaBudde-Greenspan integrator and various energy-momentum schemes adopt a difference quotient formula in their algorithmic force definitions, which suffers from numerical instability as the denominator gets close to zero. There is a need to develop structure-preserving integrators without invoking the quotient formula. In this work, the potential energy of a Hamiltonian system is split into two parts, and specially developed quadrature rules are applied separately to them. The resulting integrators can be regarded as classical ones perturbed with first- or second-order terms, and the energy split guarantees the dissipative nature in the numerical residual. In the meantime, the conservation of invariants is respected in the design. A complete analysis of the proposed integrators is given, with representative numerical examples provided to demonstrate their performance. They can be used either independently as energy-decaying and momentum-conserving schemes for nonlinear problems or as an alternate option with a conserving integrator, such as the LaBudde-Greenspan integrator, when the numerical instability in the difference quotient is detected.

Analysis of Morphological and Morphometric Changes in a Parenchymal Tissue after the Radiofrequency Ablation Procedure.

Background and Objectives: Prostate cancer is on the rise in the European Union, and radiofrequency ablation (RFA) is one of the minimally invasive treatment options used for its treatment. Therefore, the aim of this study was to investigate and analyze the effects of RFA on prostate tissues. Materials and Methods: A standard prostate RFA procedure was performed on 13 non-purebred dogs in three sessions: no cooling (NC), cooling with a 0.1% NaCl solution (C.01), and cooling using a 0.9% NaCl solution (C.09). Microtome-cut 2-3 µm sections of prostate samples were stained with hematoxylin and eosin and further examined. Results: A histopathologic evaluation identified four zones of exposure: direct, application, necrosis, and transitional, as the damage on tissues decreased going further from the ablation site. The areas and perimeters of these zones were calculated, and geometric shapes of ablative lesions were evaluated using the quotient formula. Areas and perimeters of prostate tissue lesions in the NC and C.09 sessions were of similar size, whereas those found in C.01 were statistically significantly smaller. Lesions observed in session C.01 were of the most regular geometric shape, while the most irregular ones were found in session C.09. The shapes of lesions closest to the ablation electrode were the most irregular, becoming more regular the further away from the electrode they were. Conclusions: Prostate RFA leads to tissue damage with distinct morphological zones. Notably, the prostate lesions were the smallest and the most regular in shape after RFA procedures using the 0.1% NaCl cooling solution. It can be argued that smaller ablation sites may result in smaller scars, thus allowing for faster tissue healing if the blood flow and innervation at the ablation site are not compromised.

Determination of Superior Food Crop Commodities in West Muna Regency

Food crop commodities have a role in fulfilling the need for food, feed, and domestic industry, so the development of the food crop sub-sector must be prioritized because it has competitive competitiveness. This study aims to determine the superior commodities of food crops in West Muna Regency by specifying the research's location purposively because the area can be developed for various types of food crops. The research data was obtained from the relevant agencies, namely the Agriculture Service and the Office of the West Muna Regency Statistics Agency, in 2016-2020. The data obtained were analyzed using the Location Quotient formula. The study results indicate that peanuts have an LQ value >1 compared to other food crops such as corn, rice, cassava, sweet potatoes, and soybeans. The research can be concluded that the type of food plant in the form of peanuts has the potential to be developed in Muna Regency, as seen from the value LQ>1. West Muna Regency government, in terms of the food crop sub-sector, that to make peanuts a plant with solid competitiveness in West Muna Regency, it is deemed necessary to take various development strategies that are considered feasible for the advancement of superior commodities in West Muna.

Properties on Generalized Perron Complements of Inverse N 0-matrices

For an irreducible and nonpositive matrix, we present the concepts of the Perron complement matrix and the generalized Perron complement matrix. An inequality that relates the generalized Perron complement matrices of inverse N 0-matrices is derived. In addition, we obtain the quotient formula of inverse N 0-matrices based on the quotient formula for the Schur complements.

Spatial distribution, ecological and health risk assessment of organophosphorus pesticides identified in the water of Naseri artificial wetland, Iran

Agricultural development is inevitable to meet the growing need for food. But along with this development, there are unintended and undesirable consequences for human life and the environment that need, found a solution and corrected. One of the most important adverse consequences of agricultural development is the pollution of surface and groundwater resources, which results from various factors such as soil erosion and improper use of different pesticides. This study aimed to conduct an environmental monitoring program in Naseri wetland to determine the concentrations of organophosphorus pesticides (OPPs) in water samples and also to evaluate the potential risks (ecological and health risk assessment) of these pesticides. The salting-out assisted liquid-liquid extraction method was used to extract pesticides. The residual concentrations of OPPs evaluated by gas chromatography/mass spectrometry (GC/MS). In this study, the ecological risk of OPPs calculated for wetland ecosystem, based on the acute risk quotient (RQi) formula with maximum (RQmax), mean (RQmean), and mixture (RQmix) concentrations of organophosphorus pesticides in the wetland water. Also, to assess the health risk of consuming contaminated fish with organophosphate pesticides, the potential non-carcinogenic and carcinogenic risks were determined by the hazard quotient (Index) (HQ, HI) and incremental lifetime cancer risk (ILCR) indices, respectively. The mean ± SD concentration of OPPs (Chlorpyrifos, Malathion, Ethion, Dichlorvos, Trifluralin and Diazinon) in samples of wetland water ranged from 0.14 ± 0.08 to 0.35 ± 0.12 and 0.054 ± 0.06 to 0.2 ± 0.1 (μg/L) in summer and autumn, respectively. The mean ± SD of OPPs in fish varied from 0.68 ± 0.86 to 3.94 ± 2.7 (μg/kg). Overall, the concentrations of pesticides in all water and fish samples were below the maximum residue limit (30 μg/kg) during the study period, according to the Environmental Protection Agency (EPA) and the World Health Organization (WHO). The results of acute risk quotient were in summer (RQmax = 3.49E-4 to 0.067, RQmean = 5.8E-5 to 0.029, RQmix = 0.139-0.026, 0.018-3.42E-3) and autumn (RQmax = 8E-4 to 0.051, RQmean = 7.74E-6 to 0.018 RQmix = 0.1–0.013, 6E-3- 1.5E-3). The non-carcinogenic and carcinogenic risk indexes due to fish consumption for adults and children were (HQ = 0.026-4.68E-4, HI = 0.041, ILCR = 1.7E-7) and (HQ = 1.85E-3-1.3E-5, HI = 0.041, ILCR = 5.55E-8), respectively. The risk of OPPs was generally low. But cumulative risk (pesticide mixtures), should not be ignored.

Extent of Resilience to Climate Change in Secondary Cities of Rwanda (Energy Land Use and Natural Environment): Case Study of Rusizi District

This paper titled Extent of resilience to climate change in secondary cities of Rwanda: Case study of Rusizi District. The author Evaluated the current climate related hazards and their impacts on urban livelihoods in Rusizi secondary city community. The author adopted a mixed method approach. The location quotient formula allows researcher to calculate whether a region is employing enough workers in each sector as put up against a national economy. LQ is augmented by two other pieces of information. Size of industry/cluster/occupation in terms of job and percentage of changes in LQ over period of time. A high LQ industry with a small number of jobs may be an export oriented industry otherwise, a large high LQ-industry with declining LQ over time is endangering the regional economy. The result findings revealed that Location Quotient for total employment is below 1 for manufacturing (0.99), accommodation food (0.92), public sector (0.65) primary (0.21) as well as other activities (0.87). The findings also revealed that there is a limited attention in infrastructure development and inadequate commitment in building resilience of vulnerable community to natural shocks. Recommendations include addressing infrastructure development that are resilient to climate change effects in formal and informal settlements and supporting livelihood improvement program in secondary cities and to put in place Formalized collection and recycling systems, and sanitary landfills, requiring investment in equipment, landfill development and skills of US$4-8 million by 2030 by also adopting new planning process to incorporate Green growth climate resilience principles as adopted by the GoR in 2018, by mainstreaming climate change resilience and preparedness to disaster risk management into the planning process.

A linearized ADI scheme for two-dimensional time-space fractional nonlinear vibration equations

A nonlinear initial boundary value problem with a time Caputo derivative of fractional-order and a space Riesz derivative of fractional-order is considered. A linearized alternating direction implicit (ADI) scheme for this problem is constructed and analysed. First, we use the classical central difference formula and a new -order formula to approximate the second-order derivative and the Caputo derivative in temporal direction, respectively. Meanwhile, the central difference quotient and fractional central difference formula are applied to deal with the spatial discretizations. Then, the proposed ADI scheme is proved unconditionally stable and convergent with the -order accuracy in time and the second-order accuracy in space. Furthermore, the effectiveness of the ADI scheme and theoretical findings are illustrated by numerical experiments.

Regionalization of Agricultural Based Leading Sectors and Food Security in Indonesia

Indonesia is the largest archipelago in the world with total land area is around 190 million hectares (ha), of which about 28.94 percent or some 55 million ha are agricultural land. As the world’s fourth most populous country, Indonesia’s total population is estimated to increase from about 245 million in 2013 to 288 million in 2050. This study aims to analyze the leading sectors of each province in Indonesia by Location Quotient (LQ) method and distribution of food security level in every province in Indonesia based on rice production balance. This research uses Gross Domestic Product (GDP) of Indonesia and Gross Domestic Regional Product of each of the provinces in all sectors during 2010-2014 obtained through the Indonesian Central Bureau of Statistics. The determination of the leading sectors of each province is based on the Location Quotient (LQ) which is the comparative method of the role of an economic sector in a province to the magnitude of the economic sector's role nationally. The food security index determined by the food security calculation that done by the ministry of Agriculture Indonesia especially the Food Security Agency of Indonesia based on the assumption of the resident who can fulfill more than 90 percent of Recommended Dietary Allowance (RDA) is food secure category. Leading sectors in Indonesia is varies between one province to other province. Leading sectors obtained from Location Quotient (LQ) formula shows that although it is said to be an agrarian country, the LQ results indicate that not all provinces in Indonesia have the leading sector in agriculture. Leading sector in agricultural is only found in 20 provinces out of 33 provinces in Indonesia (exclude North Kalimantan). Most provinces with agricultural based have experienced economic structuring towards secondary and tertiary sectors. Provinces with the highest LQ scores in agriculture, forestry and fisheries are found only in North Sumatra, Lampung, West Kalimantan, Central Sulawesi and West Sulawesi. Provinces with LQ> 1 score for the agricultural sector indicate that the province has a high level of agricultural production so that it becomes a comparative advantage for regional development. Agriculture, forestry and fishery sector still dominates in some parts of Indonesia, especially Sumatra, Sulawesi, Maluku, Nusa Tenggara and part of Kalimantan Island but not as major economic contributor. While most provinces in Java, Bali and Papua do not have an economic advantage in the agricultural sector. Food Security Index of Indonesia mainly classified as the moderate level except for North Maluku, Papua, and West Papua in low level and Bali and West Nusa Tenggara (NTB) in high level. Factors influencing differences in food security are based on availibility and affordability factors. Availibilty factor reflects the resilience of an area in terms of food availability, while affordability factor reflects the ease of obtaining food.

Assessment of Major Production Constraints and Common Diseases of Cattle in Selected Districts of East Wollega Zone, Western Ethiopia

This study was under taken in selected districts of east Wollega Zone of Oromia region with the objective of assessing major cattle production constraints and common cattle diseases. Questionnaire was developed and designed in a simple manner to get accurate information and pre-tested on a small group of farmers. The major cattle production constraints and common cattle diseases were identified by a pilot study and raking technique and utilized to prioritize the listed production constraints and diseases. The study districts sampled purposively whereas ‘kebeles’ or “Ganda” were selected randomly and respondents were selected using systematic random sampling techniques. Thus, a total of 90 farmers were interviewed, accordingly. A single-visit- multi-subject formal survey technique was used. Finally, the data was analyzed with SPSS statistical software and constraints were ranked and quantified using Rank Based Quotient formula. Among the six listed constraints animal feed and grazing land shortage has been assigned rank number one (82.15%) and animal health and veterinary service related problem was ranked second (81.04%). And also among the fourteen mentioned cattle diseases, diseases that ranked first, second and third were trypanosomiasis (82.65%), blackleg (60.75%), and internal and external parasites (54.9%), respectively. In conclusion, in this study animal feed and grazing land shortage and animal diseases were the main farmer’s cattle production problems. Besides, majority of farmers were practicing poor animal husbandry that creates favorable environment for the disease multiplication and distribution in the communities. Therefore, further research has to put emphasis on this prioritized production constraints using reliable tools (laboratory finding supported) and introduction of improved forage species and strengthen the fodder development practices by providing continuous training. DOI : 10.7176/JBAH/9-11-04 Publication date :June 30 th 2019

Extending a refinement of Koteljanskiĭ's inequality

The goal of this paper is two-fold. First of all, a recent refinement of Koteljanskiĭ's inequality by Dong and Hou [9] is further extended to sector matrices. Moreover, by making use of the Crabtree-Haynsworth quotient formula, we present two analogues of Yan's result [16] on 3×3 block positive definite matrices.

Simplicities of VOAs associated to Jordan algebras of type B and character formulas for simple quotients

In this paper we study the VOA VJ,r constructed by Ashihara and Miyamoto in [2], which satisfies (VJ,r)0=C1,(VJ,r)1={0}, and the Griess algebra (VJ,r)2 is isomorphic to the type B simple Jordan algebra J. We construct simple quotients V¯J,r for r∈Z≠0 using dual-pair type constructions, and we reprove that VJ,r is simple if r∉Z. We also compute the character formula of the simple quotients V¯J,r for r=−2n,n∈Z>0.

The economic impact of pilgrimage: An economic impact analysis of pilgrimage expenditures in Galicia

In this article, we calculate the economic impact of pilgrimage to Santiago de Compostela in the NUTS 2 region Galicia (Spain) in 2010. This economic impact is relevant to policymakers and other stakeholders dealing with religious tourism in Galicia. The analysis is based on the Input-Output model. Location Quotient formulas are used to derive the regional Input-Output table from the national Input-Output table of Spain. Both the Simple Location Quotient formula and Flegg’s Location Quotient formula are applied. Furthermore, a sensitivity analysis is carried out. We found that pilgrimage expenditures in 2010 created between €59.750 million and €99.575 million in Gross Value Added and between 1,362 and 2,162 jobs. Most of the impact is generated within the ‘Retail and Travel Services’ industry, but also the ‘Industry and Manufacturing’, ‘Services’ and ‘Financial and Real Estate Services’ industries benefit from pilgrimage expenditures. This research indicates that in even in the most conservative scenario, the impact of pilgrimage is significant on the local economy of Galicia.

Cluster algebras and continued fractions

We establish a combinatorial realization of continued fractions as quotients of cardinalities of sets. These sets are sets of perfect matchings of certain graphs, the snake graphs, that appear naturally in the theory of cluster algebras. To a continued fraction $[a_{1},a_{2},\ldots ,a_{n}]$ we associate a snake graph ${\mathcal{G}}[a_{1},a_{2},\ldots ,a_{n}]$ such that the continued fraction is the quotient of the number of perfect matchings of ${\mathcal{G}}[a_{1},a_{2},\ldots ,a_{n}]$ and ${\mathcal{G}}[a_{2},\ldots ,a_{n}]$. We also show that snake graphs are in bijection with continued fractions. We then apply this connection between cluster algebras and continued fractions in two directions. First we use results from snake graph calculus to obtain new identities for the continuants of continued fractions. Then we apply the machinery of continued fractions to cluster algebras and obtain explicit direct formulas for quotients of elements of the cluster algebra as continued fractions of Laurent polynomials in the initial variables. Building on this formula, and using classical methods for infinite periodic continued fractions, we also study the asymptotic behavior of quotients of elements of the cluster algebra.

Non-toric cones and Chern-Simons quivers

We obtain an integral formula for the volume of non-toric tri-Sasaki Einstein manifolds arising from nonabelian hyperkähler quotients. The derivation is based on equivariant localization and generalizes existing formulas for Abelian quotients, which lead to toric manifolds. The formula is particularly valuable in the context of AdS4 ×Y7 vacua of M-theory and their field theory duals. As an application, we consider 3d mathcal{N}=3 Chern-Simons theories with affine ADE quivers. While the  series corresponds to toric Y7, the widehat{D} and Ê series are non-toric. We compute the volumes of the corresponding seven-manifolds and compare to the prediction from supersymmetric localization in field theory, finding perfect agreement. This is the first test of an infinite number of non-toric AdS4/CFT3 dualities.

Fermionic modular categories and the 16-fold way

We study spin and super-modular categories systematically as inspired by fermionic topological phases of matter, which are always fermion parity enriched and modelled by spin topological quantum field theories at low energy. We formulate a 16-fold way conjecture for the minimal modular extensions of super-modular categories to spin modular categories, which is a categorical formulation of gauging the fermion parity. We investigate general properties of super-modular categories such as fermions in twisted Drinfeld doubles, Verlinde formulas for naive quotients, and explicit extensions of PSU(2)4m+2 with an eye towards a classification of the low-rank cases.

New linear and multilinear versions of Puhl’s quotient formula

New linear and multilinear versions of Puhl’s quotient formula

Hubungan antara Ukuran Corpus Callosum pada Anak Usia 1-5 Tahun Tanpa Kelainan MRI Otak dengan Tingkat Keparahan Keterlambatan Perkembangan Global

Background:The term,Global Developmental Delay (GDD)'is applied to children under 5 years of age and has several degrees of severity. Their MRls indicate that some of them undergo the brain abnormality and some have no abnormality. Corpus Callosum (CC) plays the role in communication line among parts of the brain, and their morphological forms are relatively stable after the kid has reached g months old. on research by Rademaker et a1.,2004, it is reported that there is a correlation between the CC size and the motoric performance on the prematurely born children. objectives: To know the correlation between the level of severity of GDD on the .l -5 year old children and no abnormality on the MRI of their brains with the size of their CC. Materials and Methods: The retrospective observation study took the data on medical records of the 1 -5 year old children in a Hospital in Surabaya since .January 2015 until March 2016, with clinical data of GDD and the examination output of brain MRI which is normal.Thirty (30) patients were found. The CC measurement was carried out at midsagittal plane of T2W image at the workstation, in genu area, midbody, splenium and its length, by two persons blindly. Data is obtained from its average value' severity level of GDD was evaluated by the developmental quotient formula, and the analysis is done by descriptive statistic and correlation test. Results: Thirty (30) patients were obtained with the same proportion of male and female (50%). severity of GDD was shown as heavy in 11 (36.vo/o),mild in 7 (13.3olo) and light in 12 (400/o).The correlation value between the severity level of GDD and the cc size is as follows: at genu (r= -0.412, p=0.024), at midbody (r= - 0.274, p= 0.143), at splenium (r = - 0.364, P = 0.048) and for length of CC ( r = -0.442, p= 0.014), (Spearman test, o=5%). Conclusion:The correlation between severity level of GDD in 1-5 year old children and the size of their CC is weak, particularly at the midbody part.The significant correlation rs shown on the genu, splenium and length of CC, but not on the midbody'The pattern of correlation is the heavier the severity level of GDD, the smaller its CC size. Keywords: corpus callosum, global developrnental delay, MRl,1-5 year old children

Reconstruction of inaccessible boundary value in a sideways parabolic problem with variable coefficients—Forward collocation with finite integration method

We investigate a sideways problem of reconstructing an inaccessible boundary value for parabolic equation with variable coefficients. Formulating the sideways problem into a sequence of well-posed direct problems (DP) and a system of Ordinary Differential Equations (ODE), we combine the recently developed finite integration method (FIM) with radial basis functions (RBF) to iteratively obtain the solution of each DP by solving an ill-posed linear system. The use of numerical integration instead of finite quotient formula in FIM completely avoids the well known roundoff-discretization errors problem in finite difference method and the use of RBF as forward collocation method (FCM) gives a truly meshless computational scheme. For tackling the ill-posedness of the sideways problem, we adapt the traditional Tikhonov regularization technique to obtain stable solution to the system of ODEs. Convergence analysis is then derived and error estimate shows that the error tends to zero when perturbation δ→0. We can then obtain highly accurate and stable solution under some assumptions. Numerical results validate the feasibility and effectiveness of the proposed numerical algorithms.

New congruences modulo powers of 2 and 3 for 9-regular partitions

Let b9(n) denote the number of 9-regular partitions of n. Recently, employing the theory of modular forms, Keith established several congruences modulo 2 and 3 for b9(n). He also presented four conjectures on b9(n) and two of them have been proved by Lin, and Xia and Yao. The remaining two conjectures are b9(32n+13)≡0(mod12) and b9(64n+13)≡0(mod24) for n⩾0. In this paper, employing 2-dissection formulas for certain quotients of theta functions, we prove that b9(32n+13)≡0(mod4) and b9(64n+13)≡0(mod8) for n⩾0. Combining these two congruences and the congruence b9(16n+13)≡0(mod3) proved by Keith, we confirm the remaining two conjectures of Keith. We also establish two infinite families of congruences modulo 9 for b9(n). For example, we prove that for all integers n⩾0 and k⩾1, b9(26kn+5×26k−1−13)≡0(mod9).