Higher congruences between newforms and Eisenstein series of squarefree level

Let $p\geq 5$ be prime. For elliptic modular forms of weight 2 and level $\Gamma_0(N)$ where $N>6$ is squarefree, we bound the depth of Eisenstein congruences modulo $p$ (from below) by a generalized Bernoulli number with correction factors and show how this depth detects the local non-principality of the Eisenstein ideal. We then use admissibility results of Ribet and Yoo to give an infinite class of examples where the Eisenstein ideal is not locally principal. Lastly, we illustrate these results with explicit computations and give an interesting commutative algebra application related to Hilbert--Samuel multiplicities.Comment: 19 pages. Minor revisions. Accepted for publication in The Journal de Th\'eorie des Nombres de Bordeau

Surfactant-assisted liquefaction of particulate carbonaceous substances

A slurry of carbonaceous particles such as coal containing an oil soluble polar substituted oleophilic surfactant, suitably an amine substituted long chain hydrocarbon, is liquefied at high temperature and high hydrogen presence. The pressure of surfactant results in an increase in yield and the conversion product contains a higher proportion of light and heavy oils and less asphaltene than products from other liquefaction processes

Coal desulfurization

Organic sulfur is removed from coal by treatment with an organic solution of iron pentacarbonyl. Organic sulfur compounds can be removed by reaction of the iron pentacarbonyl with coal to generate CO and COS off-gases. The CO gas separated from COS can be passed over hot iron fillings to generate iron pentacarbonyl

Response to "The invalidity of a Mach probe model" [Phys. Plasmas 9, 1832 (2002)]

Hutchinson gives a nice analysis of the (in)validity of Hudis and Lidsky’s unmagnetized Mach probe theory.(1) We agree with his main assertions, which are that (1) a one-dimensional model is incapable of properly describing unmagnetized ion collection by a Mach probe and (2) any experimental agreement with theories based on Hudis and Lidsky should not be interpreted as physical validation of their model

Trimerization of aromatic nitriles

Triazine compounds and cross-linked polymer compositions were made by heating aromatic nitriles to a temperature in the range of about 100 C to about 700 C, in the presence of a catalyst or mixture of catalysts. Aromatic nitrile-modified (terminated and/or appended) imide, benzimidazole, imidazopyrrolone, quinoxaline, and other condensation type prepolymers or their precopolymers were made which were trimerized with or without a filler by the aforementioned catalytic trimerization process

Electrochemical fluorination of trichloroethylene and N, N-dimethyltrifluoroacetamide

Fluorination of trichloroethylene and N, N-dimethyltrifluoroacetamide was carried out on a laboratory scale in an advanced Simons type electrochemical apparatus which could be operated automatically from ambient to 50 psi pressure. A variety of fluorine-substituted products are formed, depending upon electrolysis conditions and concentrations of reactant relative to the NaF, KF, HF electrolyte. A new reaction mechanism of electrochemical fluorination of trichloroethylene is proposed. The solvency-to-fluorine content relationship of fluorinated N, N-dimethyltrifluoroacetamide is described

Catalytic trimerization of aromatic nitriles for synthesis of polyimide matrix resins

Aromatic nitriles may be trimerized at moderate temperature and pressure with p-toluenesulfonic acid as catalyst. Studies were conducted to establish the effect of the reaction temperature, pressure, time, and catalyst concentration on yield of the trimerized product. Trimerization studies were also conducted to establish the effect of substituting electron donating or withdrawing groups on benzonitrile. Preliminary results of using the catalytic trimerization approach to prepare s-triazine cross-linked polyimide/graphite fiber composites are presented

Synthesis of ultrahigh molecular-weight poly/ethylene terrephthalate/

Solid state polymerization technology for synthesis of ultrahigh molecular weight polyethylene terephthalat