Search

The COVID-19 pandemic posed substantial challenges to healthcare systems globally and severely disrupted essential health services, including routine immunization programs. In India, these disruptions were exacerbated due to the sudden emergence of the pandemic and lockdown measures, leading to mass migrations and a shortage of healthcare workers. Caregivers’ concerns about routine immunization sessions further compounded the problem, resulting in a sharp increase in zero-dose children. This review paper examines India’s strategies for conducting one of the world’s largest COVID-19 vaccination programs while effectively restoring and perpetuating its Universal Immunization Program (UIP). The UIP played a pivotal role in sustaining immunization services during the pandemic, ultimately improving immunization coverage compared to pre-pandemic levels. India’s accomplishments in this regard are highlighted through key performance indicators, the reach of immunization services, a reduction in zero-dose children, and antigen-wise coverage. The paper also discusses the successful integration of COVID-19 vaccination within the UIP framework, underscoring the significance of existing infrastructure, technology, and capacity building. India’s dedication to concurrently managing routine immunization and COVID-19 vaccination showcases the adaptability and resilience of its healthcare system. India’s journey serves as a global example of efficient mass immunization during challenging times, emphasizing the importance of political will, healthcare infrastructure investment, skilled healthcare workforces, and comprehensive vaccination programs. In a world grappling with the dual challenge of COVID-19 and routine immunization, India’s experience provides a roadmap for strengthening healthcare systems and promoting public health as the critical agenda in challenging times.

The authors examine how consumers respond to pseudo-free offers—offers that are presented to consumers as free but that require consumers to make a nonmonetary payment (such as completing a survey or providing personal information) in order to receive the "free" good or service. Across six studies, the authors find that consumers are generally just as likely to accept pseudo-free offers (with nonmonetary costs) as comparable truly free offers (with no costs), as long as the costs of the pseudo-free offers are below some threshold. Additionally, they find that consumers are significantly more likely to accept pseudo-free offers (with nonmonetary costs) than comparable nonfree offers (with monetary costs). The authors provide evidence that consumers respond to pseudo-free offers in this way because, in general, consumers generate neutral or positive attributions for why firms make these offers, and these attributions, in turn, lead consumers to perceive the pseudo-free offers as fair. However, when contextual influences, characteristics of the pseudo-free offer, or individual dispositions increase the likelihood of negative attributions, consumers' preference for pseudo-free offers is attenuated. [ABSTRACT FROM AUTHOR]

In the Japanese language, there were various forms of address. For example, the use of the second pronoun; anata (you), kimi (you), self-name; Nakamura, Yamaguchi, kinship names; okaasan (mother), otousan (father), name of the profession; and sensei (teacher/doctor). In addition to the various address types, the zero forms of address were also known, namely the implicit use of address words. For example, address words in the form of zero were address (aisatsu); ohayou gozaimasu (good morning), irasshaimase (welcome), and sumimasen (sorry). The form of address adopted in this study was the zero-address form. This study would find the various forms and variations of zero-address. In addition, it also examined the functions and factors that influenced the use of zero-address by the sociolinguistic and pragmatics approach. This study found that there are four variations of the zero-address form, namely (1) the form of greeting; (2) the form of an exclamation or interjection; (3) the form of an interrogative sentence; and (4) the form of declarative sentences. There are two kinds of greeting, namely formal and informal. The function of the zero-address is to show respect, closeness, attract attention, and notification/statement. Factors that influence the use of zero greetings are social status, social distance, situation, and identity of the speaking actor.

Yupana Inca Tawa Pukllay (YITP) is a ludic didactic resource based on semiotic alternation that, using the reading of numbers in the Inca numeral system, improves its equivalent Indo-Arabic reading. Twelve children from first to fourth grade of a bilingual (Spanish-Quechua), multi-grade elementary school in a small rural Peruvian community were assigned an electronic tablet with YITP and learned autonomously, without teachers during the COVID-19 pandemic. The results obtained show that: (a) they learned in a very short period of time (14 min - 05h 41 min) (b) they improved digit reading accuracy on the first attempt (c) they improved digit reading speed d) they achieved a high percentage of correct reading of numbers containing at least one zero digit. The results suggest the potential of YITP as an educational tool in the teaching-learning process of arithmetic. [ABSTRACT FROM AUTHOR]

Copyright of ouvirOUver is the property of ouvirOUver 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.)

The Erdős–Lax Theorem states that, if P(z) is a polynomial of degree n having no zeros in | z | < 1 , then max | z | = 1 | P ′ (z) | ≤ n 2 max | z | = 1 | P (z) |. The problem of generalizing the Erdős–Lax Theorem to the class of polynomials having no zeros in | z | < K , K ≤ 1 is still not settled. Motivated by the above open problem, in this paper we prove some inequalities for a class of polynomials having no zeros in | z | < K , K ≤ 1 , and all these zeros lie either on a ray L emanating from the origin or zeros are symmetrically placed along this line L. Several important consequences are also discussed. Our results are the best possible and examples for the equality cases have been presented. [ABSTRACT FROM AUTHOR]

Representing the quantity zero as a symbolic concept is considered a unique achievement of abstract human thought. 1,2 To conceptualize zero, one must abstract away from the (absence of) sensory evidence to construct a representation of numerical absence: creating "something" out of "nothing." 2,3,4 Previous investigations of the neural representation of natural numbers reveal distinct numerosity-selective neural populations that overlap in their tuning curves with adjacent numerosities. 5,6 Importantly, a component of this neural code is thought to be invariant across non-symbolic and symbolic numerical formats. 7,8,9,10,11 Although behavioral evidence indicates that zero occupies a place at the beginning of this mental number line, 12,13,14 in humans zero is also associated with unique behavioral and developmental profiles compared to natural numbers, 4,15,16,17 suggestive of a distinct neural basis for zero. We characterized the neural representation of zero in the human brain by employing two qualitatively different numerical tasks 18,19 in concert with magnetoencephalography (MEG) recordings. We assay both neural representations of non-symbolic numerosities (dot patterns), including zero (empty sets), and symbolic numerals, including symbolic zero. Our results reveal that neural representations of zero are situated along a graded neural number line shared with other natural numbers. Notably, symbolic representations of zero generalized to predict non-symbolic empty sets. We go on to localize abstract representations of numerical zero to posterior association cortex, extending the purview of parietal cortex in human numerical cognition to encompass representations of zero. 10,20 • The number zero is situated on a neural number line from zero to five • Symbolic zero and non-symbolic empty sets share variance in neural representations • Cross-format representations of zero also existed on a graded number line • Cross-format zero was localized to posterior association cortex Barnett and Fleming show how non-symbolic and symbolic representations of zero are represented at the start of a neural number line and generalize across notational format. These representations are localized to the posterior association cortex. These findings provide the first account of how zero is represented in the human brain. [ABSTRACT FROM AUTHOR]

Previous work using the numerical comparison task has shown that an empty set, the nonsymbolic manifestation of zero, can be represented as the smallest quantity of the numerical magnitude system. In this study, we examined whether an empty set can be represented as such under conditions of automatic processing in which deliberate processing of stimuli magnitudes is not required by the task. In Experiment 1, participants performed physical and numerical comparisons of empty sets (i.e., empty frames) and of other numerosities presented as framed arrays of 1 to 9 dots. The physical sizes of the frames varied within pairs. Both tasks revealed a size congruity effect (SCE) for comparisons of non-empty sets. In contrast, comparisons to empty sets produced an inverted SCE in the physical comparison task, whereas no SCE was found for comparisons to empty sets in the numerical comparison task. In Experiment 2, participants performed an area comparison task using the same stimuli as Experiment 1 to examine the effect of visual cues on the automatic processing of empty sets. The results replicated the findings of the physical comparison task in Experiment 1. Taken together, our findings indicate that empty sets are not perceived as "zero," but rather as "nothing," when processed automatically. Hence, the perceptual dominance of empty sets seems to play a more important role under conditions of automatic processing, making it harder to abstract the numerical meaning of zero from empty sets. [ABSTRACT FROM AUTHOR]

In deep and high-steep formation, the first arrival wave of vertical seismic profiling (VSP) with zero well spacing appears bifurcation phenomenon or multiple wave, which makes the traditional VSP first arrival picking method unable to meet the processing requirements. Aiming at the problem of first-arrival pickup of zero-offset VSP, Numerical modeling analysis method was used to clarify the reason for the anomaly of zero offset VSP first-arrival wave in deep high and steep formation, because the formation dip angle is larger, the seismic wave far away from the wellbore reaches the geophone before the vertical incident wave through the high-speed formation, and the larger the formation dip angle is, and the greater the difference between the upper and lower medium velocities is, and the more obvious the bifurcation phenomenon is. The numerical simulation results are in agreement with the first-arrival field characteristics shown in the actual data. Then on the basis of this, a strategy of continuous downward picking along the shallow "first wave" in-phase axis based on forward modeling is proposed, which has been applied in the zero-offset VSP processing of Zhonghan 1 well in Tarim Basin and achieved good application effect. [ABSTRACT FROM AUTHOR]

Poles and zeros assignment problem by state feedbacks in positive continuous-time and discrete-time systems is analyzed. It is shown that in multi-input multi-output positive linear systems by state feedbacks the poles and zeros of the transfer matrices can be assigned in the desired positions. In the positive continuous-time linear systems the feedback gain matrix can be chosen as a monomial matrix so that the poles and zeros of the transfer matrices have the desired values if the input matrix B is monomial. In the positive discrete-time linear systems to solve the problem the matrix B can be chosen monomial if and only if in every row and every column of the n x n system matrix A the sum of n-1 its entries is less than one. Key words: assignment, pole, zero, transfer matrix, linear, positive, system, state feedback

Copyright of DIS - Dislessia, Discalculia & Disturbi di Attenzione is the property of Edizioni Centro Studi Erickson SpA 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.)

Consider a higher order state space system and associated system matrix S(λ). The aim of this paper is to linearize the system preserving system characteristics. That is, linearization preserving system characteristics (e.g, controllability, observability, various zeros and transfer function) for analysis of higher order state-space systems. In particular, we introduce Fiedler-like linearizations (Fiedler linearizations, proper generalized Fiedler (PGF) linearizations) of the system matrix S(λ) to study zeros of higher order system. Further, we show that the linearized systems are strict system equivalent to the higher order systems and hence preserve system characteristics of the original systems. We show that the PGF pencils of S(λ) provide a class of structure-preserving linearizations of S(λ). We study recovery of zero directions of higher order state space system from those of the linearizations. That is, the zero directions of the transfer functions associated to higher order state space system are recovered from the eigenvectors of the Fiedler pencils without performing any arithmetic operations. [ABSTRACT FROM AUTHOR]

Suicide continues to impact rural and regional families and communities across Australia and has become a key focus of healthcare, research, and government policy in recent years. The challenge for healthcare organizations is to translate policy visions and research for clinicians to effectively embed in day to day practice when supporting people who experience suicidal crisis. This study explored the introduction of an evidence‐based Zero Suicide framework that includes a suicide prevention pathway and training package to a rural and regional community mental health team in Victoria, Australia. A qualitative semi‐structured interview technique was used to explore the perceptions of mental health clinicians of the Zero Suicide approach, the training package and the barriers to inform its implementation across a specialist mental health service. Clinicians were complimentary of the intent of Zero Suicide and the training package and felt they had increased confidence in delivering suicide safe care. Four major themes were identified through thematic analysis: (i) Minimizing risk with realistic expectations; (ii) A good approach to making a difference; (iii) Lessons learnt; and (iv) Barriers to implementation needing to change culture. Overall participants identified the importance of continued regular suicide prevention training for all staff but also in tailoring it to different consumer and clinician needs. In addition, organizational structure and adequate staff resourcing were important to participants as was working within a safety culture. [ABSTRACT FROM AUTHOR]

In this paper I demonstrate that there is an explanation of the number marking we see on nouns when they combine with the numeral zero which combines Martí's (Semant. Pragmat., 2020a, https://doi.org/10.3765/sp.13.3) account of the morphosyntax and semantics of the numeral-noun construction with Bylinina and Nouwen's (Glossa 3(1):98, 2018) semantics for zero and which does not need to appeal to any further principles (e.g., agreement). [ABSTRACT FROM AUTHOR]

• Zero can be viewed as "nothing" or as the point between positives and negatives. • Children's conceptions of zero shifted toward a symmetry view from grades 5 to 7. • Conceptions of zero related to conceptual and procedural knowledge of integers. • Children did not appear to automatically activate magnitudes of negative integers. • A brief intervention did not change conceptions of zero or integer knowledge. The concept of zero is challenging for many children. This study investigated conceptions of zero in fifth- through seventh-grade children (N = 72) in the United States and examined how children's conceptions of zero related to other aspects of their integer knowledge. At the outset of the study, many participants held a null conception of zero (i.e., zero as "nothing"), and some participants held a conception of zero as the symmetry point between the positive and negative integers. Participants in higher grades were more likely to hold a symmetry conception. We hypothesized that participants' conceptions of zero would be related to other aspects of their integer knowledge. Relative to participants who held a null conception of zero, participants who held a symmetry conception demonstrated greater knowledge of the additive inverse principle (for every number x , there exists an inverse, − x, such that the two numbers sum to zero) and greater integer arithmetic skill. Conceptions of zero were not related to integer magnitude understanding. We also examined whether a brief lesson focusing on zero as the symmetry point would lead to shifts in participants' conceptions of zero and gains in understanding of the additive inverse principle. Participants were randomly assigned to receive a lesson about zero as null or zero as the symmetry point between positive and negative integers. Relative to the lesson about zero as null, the lesson about zero as the symmetry point did not lead to substantial changes in conceptions of zero or additive inverse knowledge. [ABSTRACT FROM AUTHOR]

This proposal report examines two issues, namely UC Merced’s effort to achieve its net zero energy 2020 Triple Zero Commitment and the lack of shade on campus. The paper works to solve these issues through the construction of a shaded walkway that is roofed with solar panels. The goal of this report is to make it clear why solving these issues is vital and to show how a shaded walkway can work to resolve the lack of shade on campus and help achieve UC Merced’s net zero energy of 2020 Triple Zero Commitment.

A new algorithm is proposed in this paper for computing the nearest polynomial to multiple given polynomials with a given zero in the real case, where the distance between polynomials is defined by the weighted ℓ 2 , q norm (0 < q ≤ 2). First, the problem is formulated as a univariate constrained non-convex minimization problem, where prior information of the coefficients of the polynomial can be embedded by selecting proper weights. Then, an iteratively reweighted algorithm is designed to solve the obtained problem, and also the convergence and rate of convergence are uniformly demonstrated for all q in (0 , 2 ]. Since all the existing methods for computing the nearest polynomial to multiple given polynomials with a given zero are limited to the real case, we ingeniously extend the results to the complex case. Finally, two representative examples that separately compute the nearest real and complex polynomials are presented to show the effectiveness of the proposed algorithm. • A weighted ℓ 2 , q -norm based minimization problem is constructed with prior information of polynomial embedded. • After converting the problem into a univariate problem, an iteratively reweighted algorithm is proposed to solve it. • Using properties of a concave function, convergence and rate of convergence of the proposed algorithm are provided. • It is the first time to study computation of the nearest polynomial to multiple given polynomials with a given zero in the complex case. [ABSTRACT FROM AUTHOR]

Copyright of Amsterdamer Beiträge zur Älteren Germanistik is the property of Brill Academic Publishers 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.)

We fill the void with our unlimited projections, which emerge from the meanderings of psyche, nourished by shadow, and shaped by personal complexes. The impact of these projections is incalculable, and our first line of defense is to block access to the void or emptiness. Accepting the presence of emptiness means emptiness symbolizes something. Understanding and giving emptiness the place of a symbol is a paradox that has intrigued people for centuries. The author provides an overview of Eastern and Western notions of nothingness and emptiness. [ABSTRACT FROM AUTHOR]

The conceptual development of natural number in preschoolers is well-researched. However, less is known about the conceptual development of zero. Recent studies suggest that children develop an understanding of zero after learning to count. It remains unclear, when a conceptual understanding of "zero" as number word for an empty set emerges. This paper integrates numerical and language theories about how, where and when the concept of zero is formed and is integrated into the class of natural numbers. The counting skills of 107 preschoolers were assessed for the number range between zero and eight as well as for their ordinal understanding of zero. The results show that compared to the natural numbers, zero was substantially more difficult. Children are able to list zero in a number word sequence (0, 1, 2, 3 .... or 3, 2, 1, 0), but were unable to describe a set as having zero numbers. This latter conception contradicts findings regarding natural numbers, in that an empty set is counter intuitive. Zero could be correctly placed when consecutive order was required, but addition and subtraction by counting was more difficult. The results suggest that the conceptual development of zero differs qualitatively from the natural numbers. Based on the results, the ordinal understanding of zero as a predecessor to one, together with its matching linguistic concepts is proposed to be the key to the conceptual development of zero. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the necessary and sufficient conditions for a polynomial P(z) to have all its zeros inside the open unit disc. These results involve two associated polynomials namely, the derivative of the reciprocal polynomial of P(z) and the reciprocal of the derivative of P(z). We also derive some generalizations of the classical Theorem of Laguerre. [ABSTRACT FROM AUTHOR]

Copyright of Desenvolvimento e Meio Ambiente is the property of Universidade Federal do Parana 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.)

The prime concern of this paper is to derive bound for the moduli of the zeros of a transcendental entire function. A few examples are given here to validate the results obtained. [ABSTRACT FROM AUTHOR]

One of the environmental problems found in developing countries, including Indonesia, is the waste problem. Waste management is the authority of the district or city government. Banyumas Regency is one of the areas that has experienced waste problems because the Final Processing Site (FPS) for its waste was closed and residents refused. In 2018, the Banyumas district received the title of waste emergency. At that time, in almost every corner of the city, there were piles of dirty and stinking garbage. Since the incident, it seems to be a whip for the local government to fix the waste problem. At present it can be said that they have been relatively successful in managing their waste, even to the point where the motto is that waste management is environmentally sound and educational. Based on that, it is interesting to study how the efforts were made and the criteria so that they dare to declare it as environmental and environmental-based waste management. The method used in this research is qualitative with interactive analysis. The results of the research show that waste management has been based on the environment with evidence in the form of; sorting waste from the source, processing which results in reducing the volume of waste at the sub-district and village level, product diversification from waste, processing into Refuse Derived Fuel (RDF) to achieve what is called zero waste. It has educational value because in the process of changing waste management through public education widely, especially in urban areas and more specifically to workers who are involved in various waste processing sites. In addition, the success of Banyumas Regency in managing waste is often used as a comparative study destination or a vehicle for education from various other local governments.

Este artigo objetiva investigar o que licenciandos em Matemática de uma Universidade Pública no interior da Bahia compreendem sobre o zero. Assim, almeja responder a seguinte questão norteadora: O que os estudantes de um curso de licenciatura em matemática compreendem sobre o número zero? A inquietação inicial dessa temática emergiu ao longo do caminhar acadêmico, que se ampliou o exercício docente, visto que existem uma gama de significados sobre o zero dos quais não são revelados no processo de ensino e aprendizagem no âmbito escolar. Para atender o objetivo desta pesquisa, foram realizadas entrevistas semiestruturadas com seis licenciandos de matemática. O procedimento metodológico deste trabalho insere-se na perspectiva qualitativa. Revela-se a luz dos dados que emergiram quatro categorias das quais sintetizam sobre a compreensão do zero.

Poles and zeros assignment problem by state feedbacks in positive continuous-time and discrete-time systems is analyzed. It is shown that in multi-input multi-output positive linear systems by state feedbacks the poles and zeros of the transfer matrices can be assigned in the desired positions. In the positive continuous-time linear systems the feedback gain matrix can be chosen as a monomial matrix so that the poles and zeros of the transfer matrices have the desired values if the input matrix B is monomial. In the positive discrete-time linear systems to solve the problem the matrix B can be chosen monomial if and only if in every row and every column of the n × n system matrix A the sum of n-1 its entries is less than one. [ABSTRACT FROM AUTHOR]

A defining characteristic of modern science is its ability to make immensely successful predictions of natural phenomena without invoking a putative god or a supernatural being. Here, we argue that this intellectual discipline would not acquire such an ability without the mathematical zero. We insist that zero and its basic operations were likely conceived in India based on a philosophy of nothing, and classify nothing into four categories—balance, absence, emptiness and nonexistence. We argue that zero is a tangible representation of nonexistence and constitutes all nonzero numbers, which together represent existence. It appears that zero's journey out of India somewhat separated its mathematical and philosophical aspects, with the former being more valued by some cultures and the latter by others. The European culture, in which modern science grew, largely ignores a philosophy of nothing due to a deep-rooted Greek philosophical base, although this science relies on the notion of nonexistence through zero. Consequently, zero is a mere number of convenience without its foundational philosophy in science, and techniques to circumvent zero are developed. We insist that, while such techniques contribute to the progress of science and mathematics within the current framework, a tendency to avoid zero and its philosophy leads to approximations and may hinder a deeper understanding. Finally, we argue that nonexistence may notionally constitute existence, and hence may be the fundamental. This implies that, if a supernatural being exists, it is not the fundamental. The independence of modern science from a supernatural being is consistent with this. [ABSTRACT FROM AUTHOR]

This paper is devoted to the problem of where the critical points of a polynomial are relative to their zeros. Classical and new developments are surveyed along with illustrative examples. The paper finishes with a short proof of the sector theorem of Sendov and Sendov. [ABSTRACT FROM AUTHOR]

While knowledge on the development of understanding positive integers is rapidly growing, the development of understanding zero remains not well-understood. Here, we test several components of preschoolers’ understanding of zero: Whether they can use empty sets in numerical tasks (as measured with comparison, addition, and subtraction tasks); whether they can use empty sets soon after they understand the cardinality principle (cardinality-principle knowledge is measured with the give-N task); whether they know what the word “zero” refers to (tested in all tasks in this study); and whether they categorize zero as a number (as measured with the smallest-number and is-it-a-number tasks). The results show that preschoolers can handle empty sets in numerical tasks as soon as they can handle positive numbers and as soon as, or even earlier than, they understand the cardinality principle. Some also know that these sets are labeled as “zero.” However, preschoolers are unsure whether zero is a number. These results identify three components of knowledge about zero: operational knowledge, linguistic knowledge, and meta-knowledge. To account for these results, we propose that preschoolers may understand numbers as the properties of items or objects in a set. In this view, zero is not regarded as a number because an empty set does not include any items, and missing items cannot have any properties, therefore, they cannot have the number property either. This model can explain why zero is handled correctly in numerical tasks even though it is not regarded as a number.

While knowledge on the development of understanding positive integers is rapidly growing, the development of understanding zero remains not well-understood. Here, we test several components of preschoolers' understanding of zero: Whether they can use empty sets in numerical tasks (as measured with comparison, addition, and subtraction tasks); whether they can use empty sets soon after they understand the cardinality principle (cardinality-principle knowledge is measured with the give-N task); whether they know what the word "zero" refers to (tested in all tasks in this study); and whether they categorize zero as a number (as measured with the smallest-number and is-it-a-number tasks). The results show that preschoolers can handle empty sets in numerical tasks as soon as they can handle positive numbers and as soon as, or even earlier than, they understand the cardinality principle. Some also know that these sets are labeled as "zero." However, preschoolers are unsure whether zero is a number. These results identify three components of knowledge about zero: operational knowledge, linguistic knowledge, and meta-knowledge. To account for these results, we propose that preschoolers may understand numbers as the properties of items or objects in a set. In this view, zero is not regarded as a number because an empty set does not include any items, and missing items cannot have any properties, therefore, they cannot have the number property either. This model can explain why zero is handled correctly in numerical tasks even though it is not regarded as a number. [ABSTRACT FROM AUTHOR]

A laboratory study was conducted to determine sodium desorption behavior from exchange positions of soil solid phase because of a quiet water flow. Using sulfuric water collected from a sulfuric spring and a chlorine water from Tigris river. The flow was through two disturbed soil columns. Soils were sampled from Fadhlia and Hamdania locations in Nineveh province/ northern Iraq. Waters flow were persisted for 240 minutes with 4 cm highness over soils surface was maintained. Leachates were collected every 10 minutes for a total ten extracts which analyzed for Na+. Three mathematical kinetic description were considered as an accumulative soluble Na+, Na+ expressed by SAR and ESP concepts , sequences as parabolic diffusion, zero order, 1st order, Elovitch and power function (poly ordered) models were applied. Mathematical descriptions revealed succession of 1st order and power function models. Na+ desorption coefficient rate values by 1st order model were ranged from 96 ×10-3 - 185 × 10-3 minute for chlorine water, for sulfuric water were from 10 ×10-3 - 34×10-3 minute for both locations respectively, while desorption coefficient rate values according to power function model were 686 ×10-3 , 683×10-3 , 634×10-3 mg.kg-1.min..-1 respectively. Results referred also that Na+ desorption coefficient rate values was proportionally increased with waters ionic strength.

Pre-Columbian Mesoamerica was a fertile crescent for the development of number systems. A form of vigesimal system seems to have been present from the first Olmec civilization onwards, to which succeeding peoples made contributions. We discuss the Maya use of the representational redundancy present in their Long Count calendar, a non-power positional number representation system with multipliers 1, 20, 18 × 20, …, 18 × 20n. We demonstrate that the Mesoamericans did not need to invent positional notation and discover zero at the same time because they were not afraid of using a number system in which the same number can be written in different ways. A Long Count number system with digits from 0 to 20 is seen later to pass to one using digits 0 to 19, which leads us to propose that even earlier there may have been an initial zeroless bijective numeration system whose digits ran from 1 to 20. Mesoamerica was able to make this conceptual leap to the concept of a cardinal zero to perform arithmetic owing to a familiarity with multiple and redundant number representation systems.

The question whether human beings process empty sets as zero has received little research attention. In this study, we used the distance and end effects as indicators for treating empty sets as a numerical entity that represents an absence of quantity. In a series of experiments, participants performed a magnitude comparison task. They were presented with empty sets and other numerosities from 1 to 9, presented as dot arrays. We manipulated task instructions relevant to the target (i.e., “choose the target that contains more/less dots” in Experiment 1) or the given numerical range mentioned in the instructions (i.e., 0–9 or 1–9 in Experiment 2) to create conditions in which an empty set would be perceived as the smallest value of the experimental numerical range. The results revealed distance effects for comparisons to empty sets, irrespective of task instructions. In Experiment 3, we manipulated the response mode. Two groups of participants responded to target location, one group with a key-press and the other vocally, while the third group responded vocally to target color. The results revealed distance effects for comparisons to empty sets only when responding to target location, regardless of the response mode, indicating that spatial features should be primed in order to perceive an empty set as a numerical entity. These findings show that perceiving an empty set as nothing or as zero depends on the context in which it is presented.

In this paper, we explore for the bicomplex version of the well known Hadamard's three circles theorem in complex analysis and also deduce its convex form. Also, the relation between zeros and poles of a bicomplex valued function is established. Moreover the Jenson's Inequality as well as some results on univalent functions are proved here in the bicomplex context. [ABSTRACT FROM AUTHOR]

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.