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About 10,000 papers for “Direct proof”

A direct proof of

Akihito Uchiyama · Springer monographs in mathematics · 2001

Cited by 0

DIRECT LIQUEFACTION PROOF OF CONCEPT

NONE · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1998

The eighth bench scale test of POC program, Run PB-08, was successfully completed from August 8 to August 26, 1997. A total of five operating conditions were tested aiming at evaluating the reactivity of different pyrolysis oils in liquefaction of a Wyoming sub-bituminous coal (Black Thunder coal). For the first time, water soluble promoters were incorporated into the iron-based GelCat to improve the dispersion of the promoter metals in the feed blend. The concentration of the active metals, Mo and Fe, was 100 and 1000 ppm of moisture-free coal, respectively. Black Thunder coal used in this run was the same batch as tested in HTI�s Run POC-02. Similar to Runs PB-01 through 7, this run employed two back mixed slurry reactors, an interstage gas/slurry separator and a direct-coupled hydrotreater. In addition to the hot vapor from the second stage separator, the first stage separator overhead liquid was also fed to the hydrotreater, which was packed with Criterion C-411 hydrotreating catalyst. Pyrolysis oil was produced off-line from a pyrolysis unit acquired from University of Wyoming. Solids rejection was achieved by purging out pressure filter solid. The recycle solvents consisted of O-6 separator bottoms and pressure filter liquid (PFL). The Run PB-08 proceeded very smoothly without any interruptions. Coal conversion consistently above 90W% was achieved. High resid conversion and distillate yield have been obtained from co-processing of coal and 343°C+ (650°F+) pyrolysis oil. Light gas (C1-C3 ) yield was minimized and hydrogen consumption was reduced due to the introduction of pyrolysis oil, compared with conventional coal-derived solvent. Catalytic activity was improved by incorporating a promoter metal into the iron-based GelCat. It seemed that lowering the first stage temperature to 435°C might increase the hydrogenation function of the promoter metal. In comparison with previous coal-waste coprocessing run (PB-06), significant improvements in the process performance were achieved due to catalyst modification and integration of pyrolysis technique into liquefaction.

Cited by 0Open access

Methods of Proof — Direct Implication

Jeremy Kun · Front Matter · 2013

I recently posted an exploratory piece on why programmers who are genuinely interested in improving their mathematical skills can quickly lose stamina or be deterred. My argument was essentially that they don't focus enough on mastering the basic methods of proof before attempting to read research papers that assume such knowledge.

Cited by 0Open access

A Direct Proof of SFIE

Alper Ünal, Sevda Özdemir, A. Köksal · IEEE Transactions on Antennas and Propagation · 2018

A simple, direct proof is given for the shifted frequency internal equivalence.

Cited by 1

Methods of Proof — Direct Implication

Jeremy Kun · Front Matter · 2013

I recently posted an exploratory piece on why programmers who are genuinely interested in improving their mathematical skills can quickly lose stamina or be deterred. My argument was essentially that they don't focus enough on mastering the basic methods of proof before attempting to read research papers that assume such knowledge.

Cited by 0Open access

A Direct Proof of Pitot’s Theorem

Quang Hung Tran · Mathematics Magazine · 2021

SummaryPitot’s theorem provides necessary and sufficient conditions for a convex quadrilateral to have an inscribed circle. There are many known proofs of this result. This paper present a new and direct proof of Pitot’s theorem using congruent triangles.

Cited by 1

Direct liquefaction proof-of-concept facility

A.G. Comolli, P. Zhou, H. Staff · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2000

The main objective of the U.S. DOE, Office of Fossil Energy, is to ensure the US a secure energy supply at an affordable price. An integral part of this program was the demonstration of fully developed coal liquefaction processes that could be implemented if market and supply considerations so required, Demonstration of the technology, even if not commercialized, provides a security factor for the country if it is known that the coal to liquid processes are proven and readily available. Direct liquefaction breaks down and rearranges complex hydrocarbon molecules from coal, adds hydrogen, and cracks the large molecules to those in the fuel range, removes hetero-atoms and gives the liquids characteristics comparable to petroleum derived fuels. The current processes being scaled and demonstrated are based on two reactor stages that increase conversion efficiency and improve quality by providing the flexibility to adjust process conditions to accommodate favorable reactions. The first stage conditions promote hydrogenation and some oxygen, sulfur and nitrogen removal. The second stage hydrocracks and speeds the conversion to liquids while removing the remaining sulfur and nitrogen. A third hydrotreatment stage can be used to upgrade the liquids to clean specification fuels.

Cited by 3Open access

A direct proof of Ramsey’s Theorem

2010

The infinite version of Ramsey’s Theorem is clearly not valid intuitionistically: even in the simple case where we color N in two colors in a recursive way, one cannot decide which color will appear infinitely often, and even less enumerate an infinite monochromatic subset. However, W. Veldman [3] found an elegant version of Ramsey’s Theorem, directly equivalent classically to

Cited by 0

Direct liquefaction proof-of-concept program

A.G. Comolli, P. Zhou, T.L.K. Lee et al. · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1997

The POC Bench Option Project (PB-Series) is geared to evaluate different novel processing concepts in catalytic direct coal liquefaction and coprocessing of organic wastes such as plastics, heavy resids, waste oils, and ligno-cellulose wastes with coal. The new ideas being explored in this program include using novel dispersed slurry catalysts and combinations of dispersed and supported catalysts (hybrid mode), and coprocessing of coal with waste plastics, low quality resids, waste oils, and ligno-cellulosic wastes, etc. The primary objective of bench run PB-07 was to study the impact of dispersed catalyst composition and loading upon the direct liquefaction performance of a high volatile bituminous Illinois No. 6 coal. The run was carried out for 20 operating days (including the four days used for the production of O-6 bottoms material for West Virginia University), spanning over five process conditions. Results are reported.

Cited by 5Open access

A direct proof of Kim's identities

R. J. Baxter · Journal of Physics A Mathematical and General · 1998

As a by-product of a finite-size Bethe Ansatz calculation in statistical mechanics, Doochul Kim has established, by an indirect route, three mathematical identities rather similar to the conjugate modulus relations satisfied by the elliptic theta constants. However, they contain factors like $1 - q^{\sqrt{n}}$ and $1 - q^{n^2}$, instead of $1 - q^n$. We show here that there is a fourth relation that naturally completes the set, in much the same way that there are four relations for the four elliptic theta functions. We derive all of them directly by proving and using a specialization of Weierstrass' factorization theorem in complex variable theory.

Cited by 7Open access

A direct proof of Tychonoff's theorem

Oliver Tatton-Brown · arXiv (Cornell University) · 2017

Proofs of Tychonoff's theorem often seem to require a bit of magic. Machinery such as ultrafilters, nets or maximal families with the finite intersection property are employed to give proofs that can be very neat, but not the kind of thing that one would naturally think of when presented with the problem (given a background in standard open set topology). Here we present a direct and pretty simple proof of Tychonoff's theorem, straight from the open cover definition of compactness.

Cited by 0Open access

DIRECT LIQUEFACTION PROOF-OF-CONCEPT PROGRAM

A.G. Comolli · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2008

This report presents the results of the bench-scale work, Bench Run PB-09, HTI Run Number 227-106, conducted under the DOE Proof-of-Concept Option Program indirect coal liquefaction at Hydrocarbon Technologies Inc. in Lawrenceville, New Jersey. Bench Run PB-09 was conducted using two types of Chinese coal, Shenhua No.2 and Shenhua No.3, and had several goals. One goal was to study the liquefaction performance of Shenhua No.2 and Shenhua No.3 with respect to coal conversion and distillate production. Another goal of Bench Run PB-09 was to study the effect of different GelCatw formulations and loadings. At the same time, the space velocity and the temperature of the fmt reactor, K-1, were varied to optimize the liquefaction of the two Chinese coals. The promoter-modified HTI GelCat{trademark} catalyst was very effective in the direct liquefaction of coal with nearly 92% maf coal conversion with Shenhua No.3 and 93% maf coal conversion with 9 Shenhua No.2. Distillate yields (CQ-524 C)varied from 52-68% maf for Shenhua No.3 coal to 54-63% maf for Shenhua No.2 coal. The primary conclusion from Bench Run PB-09 is that Shenhua No.3 coal is superior to Shenhua No.2 coal in direct liquefaction due to its greater distillate production, although coal conversion is slightly lower and C{sub 1}-C{sub 3} light gas production is higher for Shenhua No.3. The new promoter modified GelCat{trademark} proved successful in converting the two 9 Chinese coals and, under some conditions, producing good distillate yields for a coal-only bench run. Run PB-09 demonstrated significantly better performance of China Shenhua coal using HTI's coal direct liquefaction technology and GelCat{trademark} catalyst than that obtained at China Coal Research Institute (CCRI, coal conversion 88% and distillate yield 61%).

Cited by 1Open access