Uniform asymptotic approximation of diffusion to a small target: Generalized reaction models

The diffusion of a reactant to a binding target plays a key role in many biological processes. The reaction radius at which the reactant and target may interact is often a small parameter relative to the diameter of the domain in which the reactant diffuses. We develop uniform in time asymptotic expansions in the reaction radius of the full solution to the corresponding diffusion equations for two separate reactant-target interaction mechanisms: the Doi or volume reactivity model and the Smoluchowski-Collins-Kimball partial-absorption surface reactivity model. In the former, the reactant and target react with a fixed probability per unit time when within a specified separation. In the latter, upon reaching a fixed separation, they probabilistically react or the reactant reflects away from the target. Expansions of the solution to each model are constructed by projecting out the contribution of the first eigenvalue and eigenfunction to the solution of the diffusion equation and then developing matched asymptotic expansions in Laplace-transform space. Our approach offers an equivalent, but alternative, method to the pseudopotential approach we previously employed [Isaacson and Newby, Phys. Rev. E 88, 012820 (2013)PLEEE81539-375510.1103/PhysRevE.88.012820] for the simpler Smoluchowski pure-absorption reaction mechanism. We find that the resulting asymptotic expansions of the diffusion equation solutions are identical with the exception of one parameter: the diffusion-limited reaction rates of the Doi and partial-absorption models. This demonstrates that for biological systems in which the reaction radius is a small parameter, properly calibrated Doi and partial-absorption models may be functionally equivalent

Eighth year projects and activities of the Environmental Remote Sensing Applications Laboratory (ERSAL)

Projects completed for the NASA Office of University Affairs include the application of remote sensing data in support of rehabilitation of wild fire damaged areas and the use of LANDSAT 3 return beam vidicon in forestry mapping applications. Continuing projects for that office include monitoring western Oregon timber clearcut; detecting and monitoring wheat disease; land use monitoring for tax assessment in Umatilla, Lake, and Morrow Counties; and the use of Oregon Air National Guard thermal infrared scanning data. Projects funded through other agencies include the remote sensing inventory of elk in the Blue Mountains; the estimation of burned agricultural acreage in the Willamette Valley; a resource inventory of Deschutes County; and hosting a LANDSAT digital workshop

Research in remote sensing of vegetation

The research topics undertaken were primarily selected to further the understanding of fundamental relationships between electromagnetic energy measured from Earth orbiting satellites and terrestrial features, principally vegetation. Vegetation is an essential component in the soil formation process and the major factor in protecting and holding soil in place. Vegetation plays key roles in hydrological and nutrient cycles. Awareness of improvement or deterioration in the capacity of vegetation and the trends that those changes may indicate are, therefore, critical detections to make. A study of the relationships requires consideration of the various portions of the electromagnetic spectrum; characteristics of detector system; synergism that may be achieved by merging data from two or more detector systems or multiple dates of data; and vegetational characteristics. The vegetation of Oregon is sufficiently diverse as to provide ample opportunity to investigate the relationships suggested above several vegetation types

TRADE MARKS AND TRADE NAMES - MARK USED ON PATENTED ARTICLE - EFFECT OF EXPIRATION OF PATENT

P company had distributed patented razor-blades marked Enders, and, upon the expiration of its patent, registered the word as a trade mark. It also used the term Keen-Kutter, as part of its mark, but the use of this term on other goods antedated the patent by several years. P now seeks to enjoin the D company from using either term as part of its trademark. Held, (1) the word Enders having become descriptively designative of this type of razor and blade, D was entitled to use it upon expiration of P\u27s patent; (2) as to Keen-Kutter, since it was used many years before the patent and since the patent did not contribute greatly to the value of the word as a trade mark, D will be enjoined from using it as a part of his mark. Enders Razor Co. v. Christy Co., (C. C. A. 6th, 1936) 85 F. (2d) 195

TRUST MORTGAGES -- CONSTRUCTION OF NO-ACTION CLAUSE

Plaintiff, a trustee under a trust indenture securing two issues of defendant company\u27s bonds, sought to recover a partial summary judgment for interest, premiums, and principal on the series of bonds then due. Defendant company conceded that the sums claimed were overdue and unpaid, but contended that the real right of action on the bonds was vested in the bondholders. The bonds on their face made a reference to the trust indenture for a description of the rights of the holders. The bonds further contained a stipulation that, except as otherwise provided for in the trust indenture, all rights of action on the bonds were vested exclusively in the trustee. The trust indenture contained a provision that no action was to be maintained by the bondholders unless certain conditions were complied with. Held, the bonds gave sufficient notice that all rights of action were vested in the trustee. The trust indenture, to which adequate reference was made, explicitly provided that defendant was to be liable in suits by the trustees on the bonds, and that the bondholders might sue only under certain limited circumstances. Central Hanover Bank & Trust Co. v. Siemens & Halske Aktiengesellschaft, (D. C. N. Y. 1936) 15 F. Supp. 927

DAMAGES - APPLICABILITY OF GOLD CLAUSE RESOLUTION TO OBLIGATION TO DELIVER GOLD BULLION

Petitioner lessor and respondent lessee entered into a lease for the enjoyment in perpetuity of water power rights. The yearly rental was stipulated to be a quantity of gold which shall be equal in amount to fifteen hundred dollars of the gold coin of the United States of the standard of weight and fineness of the year 1894, or the equivalent of this commodity in United States currency. In 1934, after the devaluation of the dollar by the Federal Government, the lessors intervened in the lessee\u27s reorganization proceedings and filed a claim for rent. The petitioners requested that the lessees be made to pay the amount of dollars which the Government was paying for newly mined gold of the stated quantity. In behalf of the lessee the contention was that by force of the Joint Resolution of June 5, 1933, the debt was dischargeable, dollar for dollar, in the then prevailing currency. Held, the obligation was one for the payment of money and not for the delivery of gold as upon the sale of a commodity. The gold was a standard with which to stabilize the value of the dollar. In view of the circumstances which plainly showed it was a payment, the fact that it was characterized to be a commodity was of no import. The alternative provision made this conclusion inescapable. Holyoke Water Power Co. v. American Writing Paper Co., (U.S. 1937) 57 S. Ct. 485

A suggestopaedia-based method of guitar instruction

Bibliography: pages 133-138.Sight-reading is generally regarded by guitar teachers as a problem area of instruction. The aim of this thesis is to address the problem through a fourfold approach: 1. defining sight-reading in terms of its historical context ; 2. providing a rationale, and proposing an alternative method, for teaching sight-reading on the guitar based on a language teaching model ; 3. developing the proposed method ; 4. evaluating the proposed method experimentally. Music and language share many common characteristics. It is for this reason that Suggestopaedia, a method validated in language teaching, has been adapted for teaching the guitar with sight-reading skills as the central focus. Suggestopaedia has been chosen because it stimulates the whole personality, and all brain systems, of the learner