Results on energies for trees with a given diameter having perfect matching

Let Γd2nbe the set of trees with a given diameter d having a perfect matching,where 2n is the number of vertex.For a tree T in Γd2n,let Pd+1be a diameter of T and q = d m,where m is the number of the edges of perfect matching inPd+1.It can be found that the trees with minimal energy in Γd2nfor four cases q = d 2,d 3,d 4,[d2],and two remarks aregiven about the trees with minimal energy in Γd2nfor2d 33q d 5 and [d2] + 1 q2d 33 1.     

Study of factors influencing research productivity of agriculture faculty members in Iran

The purpose of this research is to analyze the relationship between individual, institutional and demographic characteristics on one hand and the research productivity of agriculture faculty members on the other. The statistical population of the research comprises 280 academic staff in agricultural faculties all over Tehran Province. The data regarding research productivity and demographic characteristics were extracted from the faculty members’ profiles. Questionnaires were utilized to collect information concerning individual and institutional variables. The reliably of the questionnaire was calculated to be between 0.74 and 0.97 using the Cronbach’s Alpha. The regression analysis revealed that from among demographic characteristics two variables, namely, academic rank and age ( \textR_\textAD ² {\text{R}}_{\text{AD}}^{ 2}  = 0.265), among individual characteristics, three variables, namely, working habits, creativity as well as autonomy and commitment ( \textR_\textAD ² {\text{R}}_{\text{AD}}^{ 2}  = 0.097), and among institutional characteristics four variables namely, network of communication with colleagues, resources of facilities, corporate management and clear research objectives ( \textR_\textAD ² {\text{R}}_{\text{AD}}^{ 2}  = 0.151) were significant predictors for agricultural faculty members’ research productivity.     

A class of not max-stable extreme value distributions

The sequences {Zi,n, l≤i≤n}, n≥l have multi-nomial distribution among i.i.d. random variables {X1,i, i≥1}, {X2,i,u≥l }, …, {Xm,i, i≥1 }. The extreme value distribution Gz(x) of this particular triangular array of i.i.d, random variables Z1,n, Z2Zn,n is discussed in this paper. We found a new type of not max-stable extreme value distributions, i) Gz(x) = r-1∏i=1ФAiαi(x) × Фαr (x);ii) Gz (x) = r-1∏i=1ψAiαi (x) × ψαr (x); iii) Gz (x) = r-1∏i=1 ∧Ai (λix) × A(x), r≥2, 0＜α1≤α2≤…≤αr and λi∈ (0,1] for i, l≤i≤r-1 which occur if Fj, …, Fm belong to the same MDA.     

A limit result for self-normalized random sums

Suppose {X, X _n ;n≥1} is a sequence i.i.d.r.v. withEX=0 andEX ²<∞. Shao (1995) proved a conjecture of Révész (1990); ifP(X=±1)=1/2, then

A new approach to the assessment of children's mathematical competence

The report is a translation of part of a Swedish paper entitled “On Students' Achievement in Mathematics after Finishing Comprehensive School”. The intention of the investigation was to

- diagnose the retention of some basic skills in some topics in algebra and geometry,

- reveal difficult steps in the learning processes in these topics.

Starting with a complicated question, e.g. the equation \(\frac{{3x - 2}}{2} = \frac{x}{3}\) a sequence consisting of 5–15 problems were constructed. Each new problem followed by the preceding one by taking away one or two details. \(\begin{gathered} 3(3x - 2) = 2x \\ {\text{ 9}}x - 6 = 2x \\ {\text{ 7}}x - 6 = 0 \\ {\text{ 7}}x = 6 \\ \end{gathered} \) is an example of a sequence belonging to the equation above. From about 10 complicated problems (“top-items”) and their sequences, in all 130 items, 10 sub-tests were put together in such a way that the pupils who took the test were not aware of the sequences but found no connection between the problems. Many surprising results were found, e.g., that the students scored higher on 14/(x+2)=2 than on 4/x=3, that the difficulty in finding the area of a triangle depended on the position of the triangle and that the problems “Simplify a/a ², a²/a, a/a” were of quite unequal difficulty. A discussion about the students' thinking in patterns and mechanically learning ends the report.     

Extreme value distributions of mixing two sequences with the same MDA

Suppose {Xi,i≥1} and {Yi, i≥1} are two independent sequences with distribution functions and , respectively. Zi,n is the combination of Xi and Yi with a probability for each I with 1≤ i≤n. The extreme value distribution GZ(x) of this particular triangular array of the i.i.d. Random variables Z1,n,… Z2,n, Zn,n is discussed. We found a new form of the extreme value distributions i)ΦAα1(x)Φα2 and ii) ψAα(x)ψα2(x)α1<α2), which are not max-stable. It occurs if FX and FY belong to the same MDA(Φ) or MDA(Ψ).     

一矩阵方程组的反射解

We derive necessary and sufficient conditions for the existence and an expression of the （anti）reflexive solution with respect to the nontrivial generalized reflection matrix P to the system of complex matrix equations AX = B and XC = D. The explicit solutions of the approximation problem min x∈Ф ｜｜X - E｜｜F was given, where E is a given complex matrix and Ф is the set of all reflexive （or antireflexive） solutions of the system mentioned above, and ｜｜·｜｜ is the Frobenius norm. Furthermore, it was pointed that some results in a recent paper are special cases of this paper.     

两个加工时间恶化的半线性平行机排序问题的启发式MBLS 算法

The combination of online or semi-online with deterioration jobs has never been researched in scheduling problems. In this paper, two semi-online parallel machine scheduling problems with linear deterioration processing time are considered. In the first problem, it is assumed that the deterioration rates of jobs are known in an interval, that is, bj ∈[0, α], where 0 〈α≤ 1 and bj denotes the linear deterioration rate. In the second problem, it is assumed that the largest deterioration rate of jobs is known in advance, that is, b = max1≤j≤n {bj }. For each of the two problems, a heuristic MBLS algorithm is worked out and its worst-case ratio is analyzed. At the same time, the worst-case ratio of the list （LS） algorithm is investigated and it is proved that all the ratios are tight.     

图的整数值控制函数

For an arbitrary subset P of the reals, a function f ： V →P is defined to be a P-dominating function of a graph G = （V, E） if the sum of its function values over any closed neighbourhood is at least 1. That is, for every v ∈ V, f（N[v]） ≥ 1. The definition of total P-dominating function is obtained by simply changing ‘closed＇ neighborhood N[v] in the definition of P-dominating function to ‘open＇ neighborhood N（v）. The （total） P-domination number of a graph G is defined to be the infimum of weight w（f） = ∑v ∈ V f（v） taken over all （total） P-dominating function f. Similarly, the P-edge and P-star dominating functions can be defined. In this paper we survey some recent progress on the topic of dominating functions in graph theory. Especially, we are interested in P-, P-edge and P-star dominating functions of graphs with integer values.     

Active on Facebook and Failing at School? Meta-Analytic Findings on the Relationship Between Online Social Networking Activities and Academic Achievement

The popularity of social networking sites (SNSs) among adolescents and young adults has raised concerns that the intensity of using these platforms might be associated with lower academic achievement. The empirical findings on this issue, however, are anything but conclusive. Therefore, we present four random-effects meta-analyses including 59 independent samples (total N = 29,337) on the association between patterns of SNS use and grades. The meta-analyses identified small negative effects of \( \widehat{\rho} \) = ??.07, 95% CI [??.12, ??.02] for general SNS use and \( \widehat{\rho} \) = ??.10, 95% CI [??.16, ??.05] for SNS use related to multitasking. General SNS use was unrelated to the time spent studying for school (\( \widehat{\rho} \) = ??.03, 95% CI [??0.11, 0.06]) and no support for the time displacement hypothesis could be found in a meta-analytical mediation analysis. SNS use for academic purposes exhibited a small positive association, \( \widehat{\rho} \) = .08, 95% CI [.02, .14]. Hypotheses with regard to cross-cultural differences were not supported.     

Attractor behavior in dilatonic （phantom） dark energy model with an especial potential

The dilaton in Weyl-Scale induced gravitational theory is regarded as a candidate of dark energy. When the potential of dilaton field is taken as the form Wσ ＋ σ^2e^-βσ2, that there exist attractor solutions to the canonical dilatonic dark energy model and the phontam model, and these attractors correspond to an equation of state ω = -1 and a cosmic density parameter Ωσ = 1, which are important features for a dark energy model and can fit with the current observations. We find a sufficient condition of the existence of a late time de Sitter attractor. The attractor behaviors, the evolutions of the state parameter ω and the cosmic density parameter Ω, the evolution of X （σ/σ0） and Y （σ/σ0^2） with respect to N（ln a）are shown numerically.     

Minus total κ-subdomination in graphs

Let G=(V, E)be a simple graph without isolated vertices. For positive integer κ, a 3-valued function f:V → {-1, 0, 1} is said to be a minus total k-subdominating function(MTκSF)if ∑u∈N(u)f(u)≥ 1 for at least κ vertices v in G, where N(v)is the open neighborhood of v. The minus total κ-subdomination number γ-κt(G)equals the minimum weight of an MTkSF on G. In this paper, the values on the minus total κ-subdomination number of some special graphs are investigated. Several lower bounds on γ-κt of general graphs and trees are obtained.     

A Geometrical Visualisation of $$\frac{ x}{1+ x} < {ln}(1+ x) < { x}-\frac{ x^2}{2(1+ x)}$$ x1+ x<ln(1+ x)< x− x22(1+ x) for x > 0

In this classroom article, we present a geometrical interpretation of a well-known inequality \(\frac{x}{1+x} < {ln}(1+x) < {x}-\frac{x^2}{2(1+x)}\) for x > 0.     

Effects of computer-aided and blended teaching strategies on students’ achievement in civic education concepts in mountain learning ecologies

The need to enhance students’ learning outcomes has become integral in secondary schools in developing countries due to increased students enrollment. Research has shown that the strategies utilized in teaching secondary school students have significant influence on their learning outcomes. At present in Nigeria, public secondary schools have not been deploying learning technologies to teach students despite the surge in enrollment. This study, therefore, determined the effects of computer-aided and blended teaching strategies on students’ achievement in civic education concepts in mountain learning ecologies. The study adopted the pretest-posttest, control group, quasi-experimental design using 3 × 2 × 3 factorial matrix. Seventy-eight students from six intact classes in secondary schools in Ondo State were selected for the study and randomly assigned to experimental and control groups. Five instruments used were: Students’ Knowledge of Civic Education Test (r = 0.78), Academic Ability Test (r = 0.72), Online and Blended Teaching Instructional Guides for experimental groups, Conventional Lecture Method Guide for the control group and Teaching Strategies Evaluation Sheet. One hypothesis was tested at 0.05 level of significance. Data was subjected to Analysis of Covariance, Estimated Marginal Means, and Scheffe’s Pairwise Comparison. There was a significant effect of treatment on students’ achievement in Civic Education concepts (F _{(2; 61)} = 4.93, p < 0.05; η ²  = .14). The students exposed to Computer-aided teaching programme had higher adjusted achievement mean score (\( \overline{x} \)= 27.86), than the blended instructional strategy group (\( \overline{x} \)= 23.06), and the control group (\( \overline{x} \)= 18.69). It was, therefore, recommended that teachers in secondary schools in mountainous locations should explore the benefits of teaching with Information and Communication Technology based strategies in civic education classrooms.     

在n维赋范空间中单位球体积及其渐进性质

Let Bnp={x ∈ Rn‖|x ‖p≤l} be the unit ball ofp norm in the n-dimensional normed space p. The formula for the volume of Bnp was obtained and its asymptotic properties were found out as n→∞and p→∞.     

On transcendental functions

Functions like log_e x, e ^x , e ^z and log_e z are defined and studied systematically. It is observed thate ^z is the only complex analytic extension of the real analytic functione ^x . It is also observed that the power (analyticity) of e^z is by choice and the beauty (its derivative is itself) of e^z is unexpected.     

Using Tasks to Explore Teacher Knowledge in Situation-Specific Contexts

Research often reports an overt discrepancy between theoretically/out-of context expressed teacher beliefs about mathematics and pedagogy and actual practice. In order to explore teacher knowledge in situation-specific contexts we have engaged mathematics teachers with classroom scenarios (Tasks) which: are hypothetical but grounded on learning and teaching issues that previous research and experience have highlighted as seminal; are likely to occur in actual practice; have purpose and utility; and, can be used both in (pre- and in-service) teacher education and research through generating access to teachers’ views and intended practices. The Tasks have the following structure: reflecting upon the learning objectives within a mathematical problem (and solving it); examining a flawed (fictional) student solution; and, describing, in writing, feedback to the student. Here we draw on the written responses to one Task (which involved reflecting on solutions of $ {\left| x \right|} + {\left| {x - 1} \right|} = 0 $ ) of 53 Greek in-service mathematics teachers in order to demonstrate the range of teacher knowledge (mathematical, didactical and pedagogical) that engagement with these tasks allows us to explore.     

Embedding Probeware Technology in the Context of Ocean Acidification in Elementary Science Methods Courses

Research indicates that preservice teacher (PT) education programs can positively impact perceptions of scientific probeware use in K-8 environments. Despite the potential of probeware to improve science instruction and student engagement, its use in elementary education has been limited. Sixty-seven PT enrolled across three sections of an elementary science methods course participated in a mixed-methods study through which they utilized probeware in a thematic experience on ocean acidification. One-way repeated measures ANOVA of pre and post survey data measuring subscales of utility, ability, and intent to use probeware demonstrated a statistically significant increase with medium to large effect sizes for all subscales across all sections \( \left(p<0.01,\kern0.5em {\eta}_p^2=0.384;\kern0.5em p<0.001,\kern0.5em {\eta}_p^2=0.517;\kern0.0em p<0.001,\kern0.0em {\eta}_p^2=0.214\right) \). Analysis of reflective journals revealed over 60% felt the multiple capabilities (notably graphing) of probeware make it a useful classroom tool, and almost one-half believed that its use makes science more enjoyable and engaging. Mapping of the unitized data from the journals on the Next Generation Science Standards suggested that probeware use especially engages learners in planning and carrying out investigations and in analyzing and interpreting data. Journals also revealed that despite PT having prior experience with probeware in science courses, its use in their future elementary classroom is conditional on having a positive experience with probeware in a science methods course. Further, embedding a probeware experience in a unit on ocean acidification provides PT with strategies for addressing climate change and engaging in argument from evidence.     

The Spelling of Vowels Is Influenced by Australian and British English Dialect Differences

Two experiments examined the influence of dialect on the spelling of vowel sounds. British and Australian children (6 to 8 years) and university students wrote words whose unstressed vowel sound is spelled i or e and pronounced /I/ or /?/. Participants often (mis)spelled these vowel sounds as they pronounced them. When vowels were pronounced similarly in both dialects (e.g., comic, with /I/; fossil, with /?/), British and Australian writers wrote the correct spelling similarly often. For vowels pronounced as /I/ in British English but /?/ in Australian English and spelled with i (e.g., muffin), British writers correctly wrote i significantly more than Australian writers. For vowels with this same pronunciation pattern but spelled instead with e(e.g., rocket), Australian writers correctly wrote e significantly more often than British writers. Dialect-related phonological differences influenced the spelling of both beginning and skilled spellers across both familiar and unfamiliar words.     

Science Letters： New solutions of shear waves in piezoelectric cubic crystals

Acoustic wave propagation in piezoelectric crystals of classes?43m and 23 is studied. The crystals Tl3VS4 and Tl3TaSe4 (43m) of the Chalcogenide family and the crystal Bi12TiO20 (23) possess strong piezoelectric effect. Because the surface Bleustein-Gulyaev waves cannot exist in piezoelectric cubic crystals, it was concluded that new solutions for shear-horizontal surface acoustic waves (SH-SAWs) are found in the monocrystals using different electrical boundary conditions such as electri- cally “short” and “open” free-surfaces for the unique [101] direction of wave propagation. For the crystal Tl3TaSe4 with coefficient of electromechanical coupling (CEMC) Ke2=e2/(C×g)～1/3, the phase velocity Vph for the new SH-SAWs can be calculated with the following formula: Vph=(Va Vt)/2, where Vt is the speed of bulk SH-wave, Vt=Vt4(1 Ke2)1/2, Va=aKVt4, aK=2[Ke(1 Ke2)1/2-Ke2]1/2, and Vt4=(C44/ρ)1/2. It was found that the CEMC K2 evaluation for Tl3TaSe4 gave the value of K2=2(Vf–Vm)/Vf～0.047 (～4.7%), where Vf～848 m/s and Vm~828 m/s are the new-SAW velocities for the free and metallized surfaces, respectively. This high value of K2(Tl3TaSe4) is significantly greater than K2(Tl3VS4)～3% and about five times that of K2(Bi12TiO20).