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Introduction: The prevalence of cardiovascular diseases increases with age in women, especially at menopause. Metabolic syndrome is one of the important factors that cause heart disease. Therefore, the importance screening of people at risk of this syndrome, especially with cheap tests, led to the introduction of new cardio metabolic indicators such as AIP, TyG and WWI. Also, due to the importance of healthy eating and physical activity in preventing metabolic syndrome, more emphasis should be placed on their use.Methods In this cross-sectional study, the number of 4732 women participating in the Hoveyzeh cohort study, after considering the entry and exit criteria, were placed into three groups: pre-menopausal (n = 736), menopausal (n = 396) and post-menopausal (n = 917).Results The prevalence of metabolic syndrome was 43.3%, 55.6%, and 62.8% in pre menopause, menopause, and post menopause, respectively. The prevalence of hypertension (50.2%), dyslipidemia (61.2%), diabetes (37.7%) and abdominal obesity according to the Iranian definition (75.9%) was higher after menopause than before menopause. Cardiovascular disease had the highest prevalence after menopause (23%). The WWI index had the highest OR among the indices with a value of 2.94 and 1.93 in menopause and after menopause, respectively. (P Conclusion Menopause leads to an increase in the prevalence of metabolic syndrome. The indices of AIP, TyG index, WWI and physical activity increase in women after menopause compared to before menopause. TyG-INDEX ،WWI ،HEI-2015 healthy eating index in this study did not show significant differences between groups after multi-regression analysis.

Water networks play an important role in complex multi-faceted water governance regimes in which the involvement of various actors could potentially lead to coherent policies. Identifying the collaborating actors and their interaction is essential for the establishment of joint water decision-making. Hence, the present study was aimed at distinguishing entities involved in water governance in Zayandeh-Rud basin, which is known as an endorheic basin in Iran. From an analytical perspective, it also tries to describe and analyze the collaborative pattern of knowledge and information exchange in the basin. Using semi-structured interview protocols, the social network data was gathered from 14 water governance-related organizations, ranging from governmental to non-governmental organizations. Identifying water governance in this basin resulted in an understanding of how human and non-human actors contribute in the practice of supply, delivery, use, and outflow processes. Moreover, considering the power relations and densities of actors' involvement in supply, delivery, use and outflow processes the integrity and coherence of the network power relations were analyzed. The power analysis findings demonstrated how the dominant role of governmental bodies and weak contribution of the private organizations and civil society resulted in up-down decision-making (on the actor component). The coherence criterion (density index) results revealed that water governance network is more coherent among the state actors within the national and extra-basin level (on the scope component). Based on the findings on the dimension component, most attention was focused on the political, administrative and economic dimensions. According to the local experience of water governance gained in this basin, practical ideas would be developed to promote water-governance in the context of transitional countries of the Middle-East.

It is known that a sequence Pi_i of permutations is quasirandom if and only if the pattern density of every 4-point permutation in Pi_i converges to 1/24. We show that there is a set S of 4-point permutations such that the sum of the pattern densities of the permutations from S in the permutations Pi_i converges to |S|/24 if and only if the sequence is quasirandom. Moreover, we are able to completely characterize the sets S with this property. In particular, there are exactly ten such sets, the smallest of which has cardinality eight., Appendices 1-5 are contained in the ancillary pdf file available on arXiv for download

Cold stress is a major environmental constraint that limits nut productivity worldwide. Late spring frost is identified as a yield-reducing factor in Persian walnut production as well. Despite significant improvements in cold and freezing tolerance methods, orchardists have not taken advantage of these recommended protection methods. This study examined determinants of walnut orchardists’ frost-protection behavior, using the extended theory of planned behavior (TPB) as a conceptual framework. Based on TPB assumptions, frost-protection behavior is mediated by a series of constructs. The purpose of this research was to examine the role of TPB variables (extended by orchard-system profile) in meeting the necessities of performing active and passive methods of frost protection. A total of 91 orchardists completed a baseline questionnaire that included the TPB constructs. The present investigation was carried out in the major walnut growing site of Sepidan County, western Fars Province, Iran. The results from the hierarchical multiple regression showed that the behavioral attitude, perceived behavioral control (PBC), intention, orchard-system profile, and interaction of orchard-system features and PBC were significant predictors of frost-protection behavior in the prospective sample. Results of the present study provided evidence that the extended TPB is a useful framework for understanding orchardists’ frost-protection behavior.

Background: Pulmonary tuberculosis ( TB) is one of the problems in diagnosis and management of patients with pneumonia and pleural effusion. Bronchoscopy and bronchoalveolar lavage (BAL) can help us in the differential diagnosis. Tumor markers are substances that are produced by cancer or other cells of the body in response to diseases. These substances can be found in the blood, urine, or body fluids, for example in bronchoalveolar lavage of some patients with pulmonary diseases. CEA is a tumor marker that can help us for diagnosis and monitoring of peripheral lung cancer. ADA has been shown to rise in the BAL of patients with TB. Because the sputum smear negative TB patients have been a diagnostic challenge for health professionals this study was designed to determine the diagnostic value of ADA & CEA & PCR in BAL fluid and then compare the relationship of these markers with sputum and clinical finding in diagnosis of pulmonary tuberculosis. Material and Method: A cross sectional study conducted in Shahrekord Hajar hospital where 100 patients were enrolled in our study (62 females, 38 males). These patients were admitted to hospital and bronchoscopy with BAL was performed, then fluid was analysed for ADA, CEA, PCR and sputum smear for TB. Result: From 100 patients who were evaluated in this study 9 patients had TB, 39 patients had pneumonia, 11 patients had primary lung malignancy, 9 patients had metastases to lung and 8 patients had bronchitis. In Patients with TB the level of ADA was not significantly elevated in BAL. ADA increased significantly in patients with pneumonia (P: 0/95). In patients with metastases to lung and primary lung cancer and a combination of both groups compared to other patients without malignancy there was no relationship between CEA. PCR was positive in TB and other patients, but significantly increased in TB. (p=0/021) Discussion: Although it was thought that CEA may be elevated in BAL of patients with malignancy and ADA in tuberculosis we did not find a correlation in these patients. This study showed that ADA and CEA levels in BAL fluid does not help us in diagnosis of TB or cancer. It may have afalse positive in pneumonia, COPD and other diseases, but PCR for TB may assist in TB diagnosis but not alone.

Komlos conjectured in 1981 that among all graphs with minimum degree at least $d$, the complete graph $K_{d+1}$ minimises the number of Hamiltonian subsets, where a subset of vertices is Hamiltonian if it contains a spanning cycle. We prove this conjecture when $d$ is sufficiently large. In fact we prove a stronger result: for large $d$, any graph $G$ with average degree at least $d$ contains almost twice as many Hamiltonian subsets as $K_{d+1}$, unless $G$ is isomorphic to $K_{d+1}$ or a certain other graph which we specify.

For a sequence $(H_i)_{i=1}^k$ of graphs, let $\textrm{nim}(n;H_1,\ldots, H_k)$ denote the maximum number of edges not contained in any monochromatic copy of $H_i$ in colour $i$, for any colour $i$, over all $k$-edge-colourings of~$K_n$. When each $H_i$ is connected and non-bipartite, we introduce a variant of Ramsey number that determines the limit of $\textrm{nim}(n;H_1,\ldots, H_k)/{n\choose 2}$ as $n\to\infty$ and prove the corresponding stability result. Furthermore, if each $H_i$ is what we call \emph{homomorphism-critical} (in particular if each $H_i$ is a clique), then we determine $\textrm{nim}(n;H_1,\ldots, H_k)$ exactly for all sufficiently large~$n$. The special case $\textrm{nim}(n;K_3,K_3,K_3)$ of our result answers a question of Ma. For bipartite graphs, we mainly concentrate on the two-colour symmetric case (i.e., when $k=2$ and $H_1=H_2$). It is trivial to see that $\textrm{nim}(n;H,H)$ is at least $\textrm{ex}(n,H)$, the maximum size of an $H$-free graph on $n$ vertices. Keevash and Sudakov showed that equality holds if $H$ is the $4$-cycle and $n$ is large; recently Ma extended their result to an infinite family of bipartite graphs. We provide a larger family of bipartite graphs for which $\textrm{nim}(n;H,H)=\textrm{ex}(n,H)$. For a general bipartite graph $H$, we show that $\textrm{nim}(n;H,H)$ is always within a constant additive error from $\textrm{ex}(n,H)$, i.e.,~$\textrm{nim}(n;H,H)= \textrm{ex}(n,H)+O_H(1)$., 24 pages, 3 figures

This series of preventative dental care community health educational materialsare openly licensed to encourage community reuse including adaptation. Oral diseases continue to disproportionately affect immigrant communities. There is a clear need for a culturally appropriate tool to enhance oral health literacy of recent immigrants. The objectives of this collaborative initiative were to develop an oral health educational tool and ensure its cultural appropriateness for newcomers. For more information or to explore collaboration opportunities for using this work for community dental education, please feel welcome to contact Dr. Maryam Amin at sharifzd@ualberta.ca.

We show that, in contrast to the integers setting, almost all even order abelian groups $G$ have exponentially fewer maximal sum-free sets than $2^{\mu(G)/2}$, where $\mu(G)$ denotes the size of a largest sum-free set in $G$. This confirms a conjecture of Balogh, Liu, Sharifzadeh and Treglown., Comment: 14 pages

The classical Corr adi-Hajnal theorem claims that every n-vertex graph G with (G) 2n=3 contains a triangle factor, when 3jn. In this paper we asymptotically determine the minimum degree condition necessary to guarantee a triangle factor in graphs with sublinear independence number. In particular, we show that if G is an n-vertex graph with (G) = o(n) and (G) (1=2 + o(1))n, then G has a triangle factor and this is asymptotically best possible. Furthermore, it is shown for every r that if every linear size vertex set of a graph G spans quadratic many edges, and (G) (1=2 +o(1))n, then G has a Kr-factor for n suciently large. We also propose many related open problems whose solutions could show a relationship with RamseyTur an theory. Additionally, we also consider a fractional variant of the Corr adi-Hajnal Theorem, settling a conjecture of Balogh-Kemkes-Lee-Young. Let t2 (0; 1) and w : E(Kn)! [0; 1]. We call a triangle in Kn heavy if the sum of the weights on its edges is more than 3t. We prove that if 3jn and w is such that for every vertex v the sum of w(e)

In 1987, Kolaitis, Promel and Rothschild proved that, for every fixed r∈N, almost every n-vertex Kr+1-free graph is r-partite. In this paper we extend this result to all functions r = r(n) with r ≤ (logn)1/4. The proof combines a new (close to sharp) supersaturation version of the Erdős-Simonovits stability theorem, the hypergraph container method, and a counting technique developed by Balogh, Bollobas and Simonovits.

Cameron and Erdős [P. Cameron and P. Erdős, Notes on sum-free and related sets, Combin. Probab.Comput., 8, (1999), 95–107] asked whether the number of maximal sum-free sets in { 1 , … , n } is much smaller than the number of sum-free sets. In the same paper they gave a lower bound of 2 ⌊ n / 4 ⌋ for the number of maximal sum-free sets. We prove the following: For each 1 ≤ i ≤ 4 , there is a constant C i such that, given any n ≡ i mod 4 , { 1 , … , n } contains ( C i + o ( 1 ) ) 2 n / 4 maximal sum-free sets. Our proof makes use of container and removal lemmas of Green [B. Green, The Cameron-Erdős conjecture, Bull. London Math. Soc., 36, (2004), 769–778; B. Green, A Szemeredi-type regularity lemma in abelian groups, with applications, Geom. Funct. Anal., 15, (2005), 340–376], a structural result of Deshouillers, Freiman, Sos and Temkin [J. Deshouillers, G. Freiman, V. Sos and M. Temkin, On the structure of sumfree sets II, Asterisque, 258, (1999), 149–161] and a recent bound on the number of subsets of integers with small sumset by Green and Morris [B. Green, R. Morris, Counting sets with small sumset and applications, Combinatorica, to appear].

Addressing a question of Cameron and Erd\Ho s, we show that, for infinitely many values of $n$, the number of subsets of $\{1,2,\ldots, n\}$ that do not contain a $k$-term arithmetic progression is at most $2^{O(r_k(n))}$, where $r_k(n)$ is the maximum cardinality of a subset of $\{1,2,\ldots, n\}$ without a $k$-term arithmetic progression. This bound is optimal up to a constant factor in the exponent. For all values of $n$, we prove a weaker bound, which is nevertheless sufficient to transfer the current best upper bound on $r_k(n)$ to the sparse random setting. To achieve these bounds, we establish a new supersaturation result, which roughly states that sets of size $\Theta(r_k(n))$ contain superlinearly many $k$-term arithmetic progressions. For integers $r$ and $k$, Erd\Ho s asked whether there is a set of integers $S$ with no $(k+1)$-term arithmetic progression, but such that any $r$-coloring of $S$ yields a monochromatic $k$-term arithmetic progression. Ne\v{s}et\v{r}il and R\"odl, and independently Spencer, answered this question affirmatively. We show the following density version: for every $k\ge 3$ and $\delta>0$, there exists a reasonably dense subset of primes $S$ with no $(k+1)$-term arithmetic progression, yet every $U\subseteq S$ of size $|U|\ge\delta|S|$ contains a $k$-term arithmetic progression. Our proof uses the hypergraph container method, which has proven to be a very powerful tool in extremal combinatorics. The idea behind the container method is to have a small certificate set to describe a large independent set. We give two further applications in the appendix using this idea., Comment: To appear in International Mathematics Research Notices. This is a longer version than the journal version, containing two additional minor applications of the container method

A spanning tree with no vertices of degree two is called a homeomorphically irreducible spanning tree (or a HIST) of a graph. In Furuya and Tsuchiya (2003), the sets of forbidden subgraphs that imply the existence of a HIST in a connected graph of sufficiently large order were characterized. In this paper, we focus on characterizing connected P 5 -free graphs which have a HIST. As applications of our main result, we also characterize forbidden pairs that imply the existence of a HIST.

Let $f(n,r)$ denote the maximum number of colourings of $A \subseteq \lbrace 1,\ldots,n\rbrace$ with $r$ colours such that each colour class is sum-free. Here, a sum is a subset $\lbrace x,y,z\rbrace$ such that $x+y=z$. We show that $f(n,2) = 2^{\lceil n/2\rceil}$, and describe the extremal subsets. Further, using linear optimisation, we asymptotically determine the logarithm of $f(n,r)$ for $r \leq 5$. Similar results were obtained by H\`an and Jim\'enez in the setting of finite abelian groups., Comment: 24 pages + 3 page appendix

Komlos conjectured in 1981 that among all graphs with minimum degree at least d, the complete graph K d + 1 minimises the number of Hamiltonian subsets, where a subset of vertices is Hamiltonian if it contains a spanning cycle. We prove this conjecture when d is sufficiently large. In fact we prove a stronger result: for large d, any graph G with average degree at least d contains almost twice as many Hamiltonian subsets as K d + 1 , unless G is isomorphic to K d + 1 or a certain other graph which we specify.

Given a graph $F$, let $s_t(F)$ be the number of subdivisions of $F$, each with a different vertex set, which one can guarantee in a graph $G$ in which every edge lies in at least $t$ copies of $F$. In 1990, Tuza asked for which graphs $F$ and large $t$, one has that $s_t(F)$ is exponential in a power of $t$. We show that, somewhat surprisingly, the only such $F$ are complete graphs, and for every $F$ which is not complete, $s_t(F)$ is polynomial in $t$. Further, for a natural strengthening of the local condition above, we also characterise those $F$ for which $s_t(F)$ is exponential in a power of $t$., Comment: 7 pages, to appear in Combinatorics, Probability and Computing

Recently, settling a question of Erd\H{o}s, Balogh and Pet\v{r}\'{i}\v{c}kov\'{a} showed that there are at most $2^{n^2/8+o(n^2)}$ $n$-vertex maximal triangle-free graphs, matching the previously known lower bound. Here we characterize the typical structure of maximal triangle-free graphs. We show that almost every maximal triangle-free graph $G$ admits a vertex partition $X\cup Y$ such that $G[X]$ is a perfect matching and $Y$ is an independent set. Our proof uses the Ruzsa-Szemer\'{e}di removal lemma, the Erd\H{o}s-Simonovits stability theorem, and recent results of Balogh-Morris-Samotij and Saxton-Thomason on characterization of the structure of independent sets in hypergraphs. The proof also relies on a new bound on the number of maximal independent sets in triangle-free graphs with many vertex-disjoint $P_3$'s, which is of independent interest., Comment: 17 pages

A method is introduced to estimate nitrogen partitioning in the structure of nanocrystalline-amorphous alloys, based on X-ray diffraction, thermogravimetry, and differential scanning calorimetery. The technique quantitatively determines the contribution of crystal interstitial sites, crystalline defects, and amorphous phase to nitrogen incorporation. Typically, the method shows that in Fe–18Cr–8Mn–2.5N alloy synthesized by mechanical alloying, about 4, 21 and 75 percent of nitrogen is distributed among the crystal interstitial sites, defects, and amorphous phase, respectively.

Mader conjectured that every $C_4$-free graph has a subdivision of a clique of order linear in its average degree. We show that every $C_6$-free graph has such a subdivision of a large clique. We also prove the dense case of Mader's conjecture in a stronger sense, i.e. for every $c$, there is a $c'$ such that every $C_4$-free graph with average degree $cn^{1/2}$ has a subdivision of a clique $K_\ell$ with $\ell=\lfloor c'n^{1/2}\rfloor$ where every edge is subdivided exactly $3$ times., 17 pages

Cameron and Erd\H{o}s raised the question of how many maximal sum-free sets there are in $\{1, \dots , n\}$, giving a lower bound of $2^{\lfloor n/4 \rfloor }$. In this paper we prove that there are in fact at most $2^{(1/4+o(1))n}$ maximal sum-free sets in $\{1, \dots , n\}$. Our proof makes use of container and removal lemmas of Green as well as a result of Deshouillers, Freiman, S\'os and Temkin on the structure of sum-free sets., Comment: 10 pages, to appear in the Proceedings of the American Mathematical Society

The study of intersecting structures is central to extremal combinatorics. A family of permutations $\mathcal{F} \subset S_n$ is \emph{$t$-intersecting} if any two permutations in $\mathcal{F}$ agree on some $t$ indices, and is \emph{trivial} if all permutations in $\mathcal{F}$ agree on the same $t$ indices. A $k$-uniform hypergraph is \emph{$t$-intersecting} if any two of its edges have $t$ vertices in common, and \emph{trivial} if all its edges share the same $t$ vertices. The fundamental problem is to determine how large an intersecting family can be. Ellis, Friedgut and Pilpel proved that for $n$ sufficiently large with respect to $t$, the largest $t$-intersecting families in $S_n$ are the trivial ones. The classic Erd\H{o}s--Ko--Rado theorem shows that the largest $t$-intersecting $k$-uniform hypergraphs are also trivial when $n$ is large. We determine the \emph{typical} structure of $t$-intersecting families, extending these results to show that almost all intersecting families are trivial. We also obtain sparse analogues of these extremal results, showing that they hold in random settings. Our proofs use the Bollob\'as set-pairs inequality to bound the number of maximal intersecting families, which can then be combined with known stability theorems. We also obtain similar results for vector spaces., Comment: 19 pages. Update 1: better citation of the Gauy--H\`an--Oliveira result. Update 2: corrected statement of the unpublished Hamm--Kahn result, and slightly modified notation in Theorem 1.6 Update 3: new title, updated citations, and some minor corrections

The main goal of this paper is to study the Hyers-Ulam-Rassias stability of the following Euler-Lagrange type additive functional equation: ∑ j = 1 m f ( − r j x j + ∑ 1 ≤ i ≤ m , i ≠ j r i x i ) + 2 ∑ i = 1 m r i f ( x i ) = m f ( ∑ i = 1 m r i x i ) , where r 1 , … , r m ∈ R , ∑ i = k m r k ≠ 0 , and r i , r j ≠ 0 for some 1 ≤ i < j ≤ m , in non-Archimedean Banach spaces. MSC:39B22, 39B52, 46S10.

We generalize the well-known Baker’s super-stability result for exponential mappings with values in the field of complex numbers to the case of an arbitrary Hilbert space with the Hadamard product. Then, we will prove an even more general result of this type. 2000 MSC: primary: 39B72, secondary: 46E40.

Cameron and Erd\H{o}s asked whether the number of \emph{maximal} sum-free sets in $\{1, \dots , n\}$ is much smaller than the number of sum-free sets. In the same paper they gave a lower bound of $2^{\lfloor n/4 \rfloor }$ for the number of maximal sum-free sets. Here, we prove the following: For each $1\leq i \leq 4$, there is a constant $C_i$ such that, given any $n\equiv i \mod 4$, $\{1, \dots , n\}$ contains $(C_i+o(1)) 2^{n/4}$ maximal sum-free sets. Our proof makes use of container and removal lemmas of Green, a structural result of Deshouillers, Freiman, S\'os and Temkin and a recent bound on the number of subsets of integers with small sumset by Green and Morris. We also discuss related results and open problems on the number of maximal sum-free subsets of abelian groups., Comment: 25 pages, to appear in the Journal of the European Mathematical Society