The articles [9], [1], [3], [4], [6], [5], [2], [7], and [8] provide the notation and terminology for this paper. We use the following convention: q, r, c, c1, c2, c3 are quaternion numbers and x1, x2, x3, x4, y1, y2, y3, y4 are elements of R. 0H is an element of H. 1H is an element of H. Next we state several propositions: (1) For all real numbers x, y, z, w holds 〈x, y, z, w〉H = x+y · i+ z · ...

We revisit old conjectures of Fermat and Euler regarding representation of integers by binary quadratic form x2 + 5y2. Making use of Ramanujan’s 1ψ1 summation formula we establish a new Lambert series identity for ∑∞ n,m=−∞ q n2+5m2 . Conjectures of Fermat and Euler are shown to follow easily from this new formula. But we don’t stop there. Employing various formulas found in Ramanujan’s noteboo...

Ahtract -Let Xi, X, , . be independent identically distributed random variables taking values in a finite set X and consider the conditional joint distribution of the first m elements of the sample Xt; . ., X, on the condition that A’, = x, and the sliding block sample average of a function h( ., .) defined on X2 exceeds a threshold OL > Eh( Xt, X2). For m fixed and M + co, this conditional joi...

The fraction, X2, of a population of D. discoideum cells competent to relay an aggregative signal has been measured as a function of time, t, spent in interphase. X2(t) is less than 0.I up to 5 h, increases slowly to 0.4 by 8 h 20 min, and saturates at I by 10 h. The hypothesis that cellular interactions might enhance X2(t) was tested by mixing populations of cells set into interphase at differ...

The 2-color Rado number for the equation x1 + x2 − 2x3 = c, which for each constant c ∈ Z we denote by S1(c), is the least integer, if it exists, such that every 2-coloring, ∆ : [1, S1(c)]→ {0, 1}, of the natural numbers admits a monochromatic solution to x1 +x2−2x3 = c, and otherwise S1(c) = ∞. We determine the 2-color Rado number for the equation x1 + x2 − 2x3 = c, when additional inequality ...

Refining some results of Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is proved that if a is a unit vector in a real or complex inner product space (H ;〈·,·〉), r,s > 0, p ∈ (0,s], D = {x ∈ H ,‖rx− sa‖ ≤ p}, x1,x2 ∈D−{0}, and αr,s = min{(r2‖x...

هدف: هدف از پژوهش حاضر مقایسۀ واکنش ­پذیری هیجانی و نظریه ذهن کودکان بر اساس سبک ­های ابرازگری مادرانشان بود. روش: روش توصیفی نوع علّی-مقایسه­ ای بود در دو گام به صورت آنلاین انجام رسید. ابتدا با استفاده نمونه ­گیری دسترس، تعداد 105 نفر مادرانی که نمرات آن­ها هر یک پرسشنامه کینگ امونز (1990)، دوسوگرایی (1990) کنترل راجر نشوور (1987) انحراف استاندارد بالاتر میانگین دست آمد (در گروه 35 نفر) دوم وا...

Results Fifty two patients (80%) were male; mean age was 62.20 ± 9.51 years; mean body mass index was 28.01 ± 4.16. The additive EuroSCORE was 3.98 ± 3.00. The low-risk group represented 33.84%, 38.46% the intermediate and 27.69% the high risk. Average length of ICU stay was 3.03 ± 4.38 days and hospital 9.64 ± 6.61 days. Analyzing the group with long stay, 63.63% were female (OR 2.40 95% CI 0....

Let X, d be a metric space and x, y ∈ X with l d x, y . A geodesic path from x to y is an isometry c : 0, l → X such that c 0 x and c l y. The image of a geodesic path is called a geodesic segment. A metric spaceX is a (uniquely) geodesic space if every two points ofX are joined by only one geodesic segment. A geodesic triangle x1, x2, x3 in a geodesic space X consists of three points x1, x2, x...

In the process of profiling the secondary metabolites of actinobacteria isolated from the Saudi coastal habitats for production of antibiotics and anti-cancer drugs, the cultures of strain WH1 that was identified as Streptomyces heliomycini exhibited strong antibacterial activity against Staphylococcus aureus. By means of MS and NMR techniques, the active compounds were characterized as actinom...