Skorohod and rough integration for stochastic differential equations driven by Volterra processes

Given a solution Y to a rough differential equation (RDE), a recent result [7] extends the classical Ito-Stratonovich formula and provides a closed-form expression for ∫ Y ○ dX − ∫ Y dX, i.e. the difference between the rough and Skorohod integrals of Y with respect to X, where X is a Gaussian process with finite p-variation less than 3. In this paper, we extend this result to Gaussian processes with finite p-variation such that 3 ≤ p 1/4. As an application we recover Ito formulas in the case where the vector fields of the RDE governing Y are commutative

Preserving Competition: Economic Analysis, Legal Standards and Microsoft

In a recent symposium issue of the George Mason Law Review, Steven Salop and R. Craig Romaine use the Microsoft litigation as a focus for discussion of antitrust law. Salop and Romaine argue that each of the allegations against Microsoft could constitute evidence of a design by Microsoft to reduce competition and to preserve or extend monopoly power. They argue as well that the right legal standard to apply in monopolization cases is a competitive effects test that balances the benefits and harms of the monopolist\u27s conduct. This article exposes problems with their approach, explains why it departs from current antitrust standards, and urges an approach consistent with current standards

Antitrust Intent

Many legal rules turn on a party\u27s state of mind or intent with respect to some action or consequence. Legal scholars have long debated the contours of such requirements and the sorts of proof required for them. Intent has been an especially controversial issue in antitrust law. This paper provides a theory of legal standards that explains the role of intent analysis in antitrust and in other areas of the law. We argue that intent requirements, and many other legal rules, can be understood by focusing on the goal of minimizing the expected costs from legal errors. After developing a positive theory of intent standards, we apply the theory to antitrust to show that it explains both the allocation of and proof requirements for the specific intent standards in antitrust doctrine. We then use the Microsoft case as a concrete study of the function of intent rules in antitrust

Sn-modification of Pt7/alumina model catalysts: Suppression of carbon deposition and enhanced thermal stability.

An atomic layer deposition process is used to modify size-selected Pt7/alumina model catalysts by Sn addition, both before and after Pt7 cluster deposition. Surface science methods are used to probe the effects of Sn-modification on the electronic properties, reactivity, and morphology of the clusters. Sn addition, either before or after cluster deposition, is found to strongly affect the binding properties of a model alkene, ethylene, changing the number and type of binding sites, and suppressing decomposition leading to carbon deposition and poisoning of the catalyst. Density functional theory on a model system, Pt4Sn3/alumina, shows that the Sn and Pt atoms are mixed, forming alloy clusters with substantial electron transfer from Sn to Pt. The presence of Sn also makes all the thermally accessible structures closed shell, such that ethylene binds only by π-bonding to a single Pt atom. The Sn-modified catalysts are quite stable in repeated ethylene temperature programmed reaction experiments, suggesting that the presence of Sn also reduces the tendency of the sub-nano-clusters to undergo thermal sintering

Further experiements on the control of early blight or target spot of potatoes

The effective control of Potato Early Blight or Target Spot by the use of Zineb fungicide (used in the proprietary form Dithane Z.78) has previously been reported in this Journal. It was shown in preliminary spray trials that the foliage blight caused by this disease is very destructive, and by the application of four Dithane sprays yields were increased in the order of 30 per cent., equivalent to approximately four tons per acre. Further experiments have now been conducted and the results indicate that even two applications of Dithane spray may, under conditions of severe blight attack, promote worthwhile higher yields

Plant disease - early blight or target spot of potatoes

Early blight or target spot caused by the fungus Alternaria solani is a widespread disease of potatoes which in Western Australia is most prevalent in crops dug in autumn and early summer. The disease may attack both foliage and tubers, but the tuber rot phase of the disease has hitherto caused most concern to local growers because it causes obvious losses in storage. The less obvious but more serious effects of the foliage blight have generally been overlooked, chiefly because the disease usually develops late in the season when the crops are approaching maturity. However recent spray trials with new fungicides have clearly demonstrated that the destructiveness of the foliage attack has been greatly underestimated, for it may cause considerable reduction in yield

Understanding the Impact of Learning Community Support for STEM students with Low Mathematics Placement

As a residential college within Michigan State University that focuses on STEM fields, Lyman Briggs College developed a STEM learning community to support students with low mathematics placement test scores, the Instilling Quantitative and Integrative Reasoning program (INQUIRE). INQUIRE serves some of those students considered historically at-risk based on STEM retention and graduation rates. INQUIRE was developed as learning community using curricular design, cohort-building activities, and academic resources to assist students’ transition to college. Participating students were surveyed to understand the student experience of INQUIRE. Students’ responses indicated that the program helped them adjust to college, prepare for introductory STEM courses, collaborate with other students and faculty, and experience academic and personal growth. A few students (4%) stated that the program put them behind their peers. Quantitatively, four-year STEM retention showed an increase from 43 to 56% for students starting in college-level algebra but remained statistically unchanged for those beginning in pre-college algebra (moving from 31 to 37%). The six-year graduation rates for both groups remained unchanged. These results indicate the difficulty in improving the graduation rates of students with low mathematics placement but indicate that INQUIRE made a positive and meaningful impact on students’ experience