On the properties of Newton-Euler pairs

If and are two sequences such that a₁=b₁ and , then we say that (a_n,b_n) is a Newton-Euler pair. In the paper, we establish many formulas for Newton-Euler pairs, and then make use of them to obtain new results concerning some special sequences such as and B_n, where p(n) is the number of partitions of n, σ(n) is the sum of divisors of n, and B_n is the nth Bernoulli number.     

A search for spontaneous emission of heavy clusters in the 127I nuclide

The results of an experimental search for spontaneous cluster decay in ¹²⁷I are presented. Several possible channels have been investigated considering an exposure of 33834 kg ^. day collected by a large-mass highly radiopure NaI(Tl) set-up deep underground in the Gran Sasso National Laboratory of the INFN. New lower limits on the lifetime of ²⁴₁₀Ne, ²⁸₁₂Mg, ³⁰₁₂Mg, ³²₁₄Si, ³⁴₁₄Si, ⁴⁸₂₀Ca, ⁴⁹₂₁Sc cluster radioactivity in ¹²⁷I have been achieved.     

Universal Kummer congruences mod prime powers

We have previously proved Kummer congruences mod primes p such that for the universal divided Bernoulli numbers . In this paper we strengthen these congruences to hold mod powers of p.     

Dense Minors In Graphs Of Large Girth

We show that a graph of girth greater than 6 log k+3 and minimum degree at least 3 has a minor of minimum degree greater than k. This is best possible up to a factor of at most 9/4. As a corollary, every graph of girth at least 6 log r+3 log log r+c and minimum degree at least 3 has a K _r minor.     

Synthesis of Mesoporous Silica Materials via Nonsurfactant Templated Sol-Gel Route by Using Mixture of Organic Compounds as Template

Mesoporous silica materials have been successfully prepared by employing a mixture of -cyclodextrin and urea as a template in a HCl-catalyzed sol-gel process, followed by extraction with water. The obtained materials are characterized by nitrogen adsorption-desorption measurements, powder X-ray diffraction patterns and transmission electron microscopy. The changes of the pore parameters depend on both the weight ratio of -cyclodextrin and urea and the template content in the final silica composite. The effects of the mixture as template (or pore-forming agent) on the physicochemical properties of the two synthesized systems, with different weight ratio and same template content, as well as varied template content and fixed weight ratio, were investigated in this paper. The results show that the hydrogen bonding interactions between -cyclodextrin and urea molecules or urea aggregates, the urea-holding -cyclodextrin molecules themselves as well as inorganic species are the driving force in the formation of mesoporous silica materials.     

Subdivisions of a Graph of Maximal Degree n + 1 in Graphs of Average Degree and Large Girth

Dedicated to the memory of Paul Erdős It is proved that for every finite graph H of maximal degree and every , there is an integer such that every finite graph of average degree at least and of girth at least contains a subdivision of H. Received May 5, 1999     

Filterable Agents for Hyperpolarization of Water,Metabolites, and Proteins

Hyperpolarization is generated by dissolution dynamic nuclear polarization (d‐DNP) using a polymer‐based polarizing agent dubbed FLAP (filterable labeled agents for polarization). It consists of a thermo‐responsive poly(N‐isopropylacrylamide), also known as pNiPAM‐COOH, labeled with nitroxide radicals. The polymer powder is impregnated with an arbitrary solution of interest and frozen as is. Dissolution is followed by a simple filtration, leading to hyperpolarized solutions free from any contaminants. We demonstrated the use of FLAP to hyperpolarize partially deuterated water up to P(¹H)=6 % with a long relaxation T₁ >36 s characteristic of high purity. Water hyperpolarization can be transferred to drugs, metabolites, or proteins that are waiting in an NMR spectrometer, either by exchange of labile protons or through intermolecular Overhauser effects. We also show that FLAPs are suitable polarizing agents for ¹³C‐labeled metabolites such as pyruvate, acetate, and alanine.     

OBSERVATIONAL COSMOLOGY AND NUMERICAL RELATIVITY

Abstract

This paper brings together the theory of observational cosmology and the null-cone characteristic initial value problem (CIVP) of numerical relativity. A computer code is constructed which calculates the past behaviour of the Universe from input data that is, in principle, measurable. For practical reasons the code is limited to the case of axisymmetry without rotation. The construction of the code brings to light an interesting general point about observational cosmology. In a big-bang universe it is impossible, even in principle, to determine the state of the universe at early times. For the Einstein-de Sitter model this limit is t ₀/27, where t ₀ means now.     

Optimization of the determination of chemical oxygen demand in wastewaters

Chemical oxygen demand (COD) is one of the most relevant chemical parameters for the management of wastewater treatment facilities including the control of the quality of an effluent. The adequacy of decisions based on COD values relies on the quality of the measurements. Cost effective management of the minor sources of uncertainty can be applied to the analytical procedure without affecting measurement quality. This work presents a detailed assessment of the determination of COD values in wastewaters, according to ISO6060:1989 standard, which can support reduction of both measurement uncertainty and cost of analysis. This assessment includes the definition of the measurement traceability chain and the validation of the measurement procedure supported on sound and objective criteria. Detailed models of the measurement performance, including uncertainty, developed from the Differential Approach, were successfully validated by proficiency tests. The assumption of the measurement function linearity of the uncertainty propagation law was tested through the comparison with the numerical Kragten method. The gathered information supported the definition of strategies for measurement uncertainty or cost reduction. The developed models are available as electronic supplementary material, in an MS-Excel file, to be updated with the user's data.