Let
P
be a positive rational number. A function
f
:
R
→
R
has the
finite gaps property mod P
if the following holds: for any positive irrational
α
and positive integer
M
, when the values of
f
(
m
α
...)
,
1
≤
m
≤
M
, are inserted mod
P
into the interval 0,
P
) and arranged in increasing order, the number of distinct gaps between successive terms is bounded by a constant
k
f
which depends only on
f
. In this note, we prove a generalization of the 3d distance theorem of Chung and Graham. As a consequence, we show that a piecewise linear map with rational slopes and having only finitely many non-differentiable points has the finite gaps property mod
P
. We also show that if
f
is the distance to the nearest integer function, then it has the finite gaps property mod 1 with
k
f
≤
6
.
AbstractSales promotion is a common marketing approach used in the clothing industry to attract customers and increase sales, resulting in the effect of sales promotions on consumer purchasing ...behavior. Discounts, coupons, flash sales, and loyalty bonuses are all forms of sales promotions. Advertising and marketing of a product increase its reach to more people. The present study looks at how sales promotions influence customer purchasing behavior in the apparel business. The study investigates several sales promotion tactics to attract consumers that can influence consumer decisions in the apparel business. The methodology of the paper is based on a statistical analysis of close-ended questionnaire responses from 330 people aged 18–35 residing in India, as part of field research. The current study asked respondents questions on a 5-point Likert scale. The replies were evaluated using statistical tools from Microsoft, such as Excel, and IBM's Statistical Package for Social Science, as well as statistical techniques such as Regression and Pearson Correlation. According to the study’s findings, sales promotions have a positive influence on customer purchase decisions in India’s apparel industry. Discounts and coupons add up to savings and have a favorable impact on customer purchasing patterns.
•Dynamic micelles of 4-dodecylbenzenesulfonic acid (DBSA) at below < 75 mM.•Very stable micelles of DBSA at higher concentrations (>75 mM).•Efficiency of dynamic DBSA micelles in micellar catalysis ...in water.•Less activity of vesicles and stable micelles of DBSA in micellar catalysis.•Importance of molecular packing of DBSA at interface in micellar catalysis.
The 4-dodecylbenzenesulfonic acid (DBSA), a Brønsted acid surfactant combined catalyst, forms micelles and vesicles in water. The dynamic DBSA micelles, which are present at lower concentrations (<75 mM), are more efficient in micellar catalysis in water. The dynamic micelles supply high flux of monomers to emulsify the water-insoluble/ non-polar reactant in water creating huge interface. The large intermolecular distance between DBSA at interface of emulsions provides appropriate microenvironment for the reaction (space to accommodate the molecules of reactant(s) and reaction intermediates, and accessible H+ ions). At higher concentrations (>75 mM), micelles become very stable, which have good solubilization capacity for the water-insoluble reactant. However, the stable micelles are less active in micellar catalysis due to the close molecular packing of DBSA strongly solubilizing the reactant(s) and reducing the accessibility of H+ ions due to extensive hydrogen bonding between –SO3H groups.
Significant advancement has occurred over the years in diagnosis, recognition, intervention and impact of acute kidney injury (AKI) on morbidity and mortality in critically-ill neonates. However an ...increased risk of chronic kidney disease (CKD) is still observed among neonates who survive an episode of AKI. Therefore, preventing and adequately managing AKI in neonates could help in controlling long-term renal morbidity in neonates who develop AKI. Thus, this study was undertaken with the aim of studying the incidence, contributing factors and outcomes of AKI in at-risk term neonates admitted to the neonatal intensive care unit (NICU).
One hundred and ninety-six term neonates admitted to the NICU with sepsis, hypoxic ischemic encephalopathy (HIE), dehydration and respiratory distress were enrolled and evaluated over a period of one year. Detailed maternal history along with neonatal history, anthropometry, vitals and clinical signs of neonates were recorded in a pretested proforma. Urine output was measured in all at-risk neonates. Serum creatinine was estimated to categorize AKI into stages as per modified KDIGO criteria.
Incidence of AKI was 21%, (n = 107 out of 510 admissions) in the study. Mortality was significantly higher in AKI stage III neonates (88.9%) (p < 0.001). Multivariate analysis revealed that hypoxic ischemic encephalopathy (HIE) had 35.293 (p < 0.001) times higher risk, while sepsis had 35.701 (p < 0.001), dehydration had 30.260 times (p < 0.001) and respiratory distress had 10.366 times (p < 0.001) higher risk of developing AKI.
Our study recorded a high incidence of AKI among at-risk neonates. KDIGO criteria for diagnosing AKI is feasible to apply in the at-risk neonates and helps in its early identification. Early diagnosis and timely intervention in neonates with HIE, sepsis, dehydration and respiratory can prevent the progression of AKI and thus improve prognoses.
Diabetes has become the epidemic of the 21st century, and with over 90% patients with diabetes becoming at a risk of developing retinopathy, diabetic retinopathy has emerged as a major public health ...concern. In spite of cutting edge research in the field, how retina and its vasculature are damaged by the diabetic milieu remains ambiguous. The environmental factors, life style or disease process can also bring in modifications in the DNA, and these epigenetic modifications either silence or activate a gene without altering the DNA sequence. Diabetic environment up- or downregulates a number of genes in the retina, and emerging research has shown that it also facilitates epigenetic modifications. In the pathogenesis of diabetic retinopathy, the genes associated with important enzymes (e.g., mitochondrial superoxide dismutase, matrix metalloproteinase-9 and thioredoxin interacting protein) and transcriptional factors are epigenetically modified, the enzymes responsible for these epigenetic modifications are either activated or inhibited, and the levels of microRNAs are altered. With epigenetic modifications taking an important place in diabetic retinopathy, it is now becoming critical to evaluate these modifications, and understand their impact on this slow progressing blinding disease.
In diabetic retinopathy, increased cytosolic reactive oxygen species, produced by NADPH oxidase (Nox), damage mitochondria, and this accelerates apoptosis of retinal capillary cells, resulting in the ...histopathology. Activation of Nox2 is mediated by a small molecular weight GTPase, Rac1, and retinal Rac1 is activated in diabetes. Our goal is to investigate the molecular mechanism responsible for transcriptional activation of Rac1 in the development of diabetic retinopathy. Using retinal microvessels, the site of histopathology associated with diabetic retinopathy, from streptozotocin-induced diabetic rats, we investigated the binding of the nuclear transcriptional factor-kB (NF-kB) at Rac1 promoter. Since activation of NF-kB is regulated by its acetylation-deacetylation, the role of acetylation in Rac1 transcription was confirmed in the retina from diabetic mice overexpressing a deacetylase, Sirtuin 1. Diabetes increased the binding of p65 subunit of NF-kB at the Rac1 promoter. Overexpression of Sirtuin 1 prevented hyper-acetylation of p65, decreased its binding at the Rac1 promoter and ameliorated Rac1-Nox2 mediated mitochondrial damage. Thus, in diabetes Rac1 transcriptional activation in the retina is mediated by acetylation of NF-kB, and modulation of acetylation during the early stages of diabetic retinopathy has potential to inhibit/retard its development.
•Transcription of retinal Rac1 in diabetes is regulated by NF-kB.•Hyperacetylation of NF-kB increases its binding at Rac1 promoter.•Overexpression of deacetylase, Sirt1, prevents diabetes-induced increase in Rac1.•Rac1, via Nox2-ROS, damages mitochondria, initiating a futile cycle of ROS.•Regulation of Sirt1 should ameliorate development of diabetic retinopathy.
An elastic organic crystal, 2,6-dichlorobenzylidine-4-fluoro-3-nitroaniline (DFNA), which also shows thermosalient behavior, is studied. The presence of these two distinct properties in the same ...crystal is unusual and unprecedented because they follow respectively from isotropy and anisotropy in the crystal packing. Therefore, while both properties lead from the crystal structure, the mechanisms for bending and thermosalience are quite independent of one another. Crystals of the low-temperature (α) form of the title compound are bent easily without any signs of fracture with the application of deforming stress, and this bending is within the elastic limit. The crystal structure of the α-form was determined (P21/c, Z = 4, a = 3.927(7) Å, b = 21.98(4) Å, c = 15.32(3) Å). There is an irreversible phase transition at 138 °C of this form to the high-temperature β-form followed by melting at 140 °C. Variable-temperature X-ray powder diffraction was used to investigate the structural changes across the phase transition and, along with an FTIR study, establishes the structure of the β-form. A possible rationale for strain build-up is given. Thermosalient behavior arises from anisotropic changes in the three unit cell parameters across the phase transition, notably an increase in the b axis parameter from 21.98 to 22.30 Å. A rationale is provided for the existence of both elasticity and thermosalience in the same crystal. FTIR studies across the phase transition reveal important mechanistic insights: (i) increased π···π repulsions along 100 lead to expansion along the a axis; (ii) change in alignment of C–Cl and NO2 groups result from density changes; and (iii) competition between short-range repulsive (π···π) interactions and long-range attractive dipolar interactions (C–Cl and NO2) could lie at the origin of the existence of two distinctive properties.
Synthesis of highly active nano-crystalline, thermally stabilized solid acid catalyst has been reported by loading different weight fractions of sulfated zirconia on chemically activated fly ash ...through two step sol–gel technique. The catalysts were characterized using powder XRD, FT-IR, N
2-adsorption desorption study, CHNS elemental analysis, SEM-EDAX and their acidity were measured by pyridine adsorbed FTIR. Liquid phase benzylation of benzene and toluene with benzyl chloride was studied as test reaction for catalytic activity of SZF catalysts. A very high conversion of benzene (87%) and toluene (93%) were observed, which is attributed to significant amount of acid site on the catalyst surface. The FTIR study of the pyridine adsorbed samples reflects the presence of Brønsted as well as Lewis acid sites. The catalyst with 12
wt.% zirconia (SZF-12) was regenerated and reused up to four reaction cycles with equal efficiency as in the first run.
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