A theological aim historical assessment of the Christology of Nestorius in the context of his times

The Patriarch Nestorius was condemned as an heretic at the Councils of Ephosus and Chalcedon. During the last century, following the rediscovery of many of his writings, several important scholars have examined his case. Their conclusions have varied considerably; on the whole they have been too kind to him. This thesis begins by examining the life of Nestorius to put the controversies in context. In particular, the question of whether he was still alive at the time of Chalcedon is examined; also the length of tine he spent in exile. Certainly he was alive until shortly before the Council met, but that is all we can say with certainly. Following this discussion, the historical reasons for the condemnation of Nestorius are treated. The political and sociological controversies between Alexandria, Constantinople, Rome, Antioch and Jerusalem are examined, together with the differences between the Antiochene and Alexandrian schools of theology. Personality and group conflicts no doubt played their part, but could not have led to Nestorius' condemnation on their own. A major section of the thesis is concerred with the Christology of the main theological schools. Their concepts are examined and the variations among individual representatives of the Antiochene school particularly are examined. All this helps to set Nestorius' work in context. After a short critical chapter on the literary Mstory of Nestorius' writings, including references to Abramowski's recent work on a dual-authorship hypothesis of the Book of Heracleides, we turn to Nestorius' own thought and vocabulary. The conclusion reached suggests that although Nestorius' intentions were good, and that he rendered good service by safeguarding the humanity of Christ, be ended up in a cul-de-sac, when it came to establishing the unity of Christ's person in the Prosopon. We also conclude that the Book of Heracleides did little or nothing to help his case

Numerical studies for fractional functional differential equations with delay based on BDF-type shifted Chebyshev approximations

Fractional functional differential equations with delay (FDDEs) have recently played a significant role in modeling of many real areas of sciences such as physics, engineering, biology, medicine, and economics. FDDEs often cannot be solved analytically so the approximate and numerical methods should be adapted to solve these types of equations. In this paper we consider a new method of backward differentiation formula-(BDF-) type for solving FDDEs. This approach is based on the interval approximation of the true solution using the Clenshaw and Curtis formula that is based on the truncated shifted Chebyshev polynomials. It is shown that the new approach can be reformulated in an equivalent way as a Runge-Kutta method and the Butcher tableau of this method is given. Estimation of local and global truncating errors is deduced and this leads to the proof of the convergence for the proposed method. Illustrative examples of FDDEs are included to demonstrate the validity and applicability of the proposed approach. © 2015 V. G. Pimenov and A. S. Hendy

University of Waikato radiocarbon dates I

This date list reports on samples submitted by University of Waikato researchers and assayed in the Waikato laboratory mainly between 1979 and 1985. Most dates reported here relate to the deposition of distal airfall tephras in lakes and peats in central and northern North Island, New Zealand. Most of the tephras have been correlated with named eruptive units elsewhere using diagnostic mineralogic and chemical criteria, together with stratigraphic and age relationships.The dates listed in Section 2 were obtained on carbonaceous matter associated with the Hinuera Formation, an extensive low-angle fan of volcanogenic alluvium that was deposited in several phases in the Waikato and Hauraki basins before and during the last stale (isotope stage 2) of the last glaciation. In Section 3, the samples comprise materials associated with peat bog growth or local sedimentation that postdates the deposition of the Hinuera Formation, ie, < ca 15,000 BP. Samples in both Sections 2 and 3 are grouped into series according to geographic location, and, where appropriate, arranged stratigraphically with uppermost samples shown first

Serine protease inhibitors serpina1 and serpina3 are down-regulated in bone marrow during hematopoietic progenitor mobilization

Mobilization of hematopoietic progenitor cells into the blood involves a massive release of neutrophil serine proteases in the bone marrow. We hypothesize that the activity of these neutrophil serine proteases is regulated by the expression of naturally occurring inhibitors (serpina1 and serpina3) produced locally within the bone marrow. We found that serpina1 and serpina3 were transcribed in the bone marrow by many different hematopoietic cell populations and that a strong reduction in expression occurred both at the protein and mRNA levels during mobilization induced by granulocyte colony-stimulating factor or chemotherapy. This decreased expression was restricted to the bone marrow as serpina1 expression was maintained in the liver, leading to no change in plasma concentrations during mobilization. The down-regulation of serpina1 and serpina3 during mobilization may contribute to a shift in the balance between serine proteases and their inhibitors, and an accumulation of active neutrophil serine proteases in bone marrow extravascular fluids that cleave and inactivate molecules essential to the retention of hematopoietic progenitor cells within the bone marrow. These data suggest an unexpected role for serpina1 and serpina3 in regulating the bone marrow hematopoietic microenvironment as well as influencing the migratory behavior of hematopoietic precursors

Numerical discretization for fractional differential equations with feedback control

In this paper, we introduce a numerical scheme for fractional differential equations with feedback control. Due to the possibility of dealing with a feedback control as a functional delay, we construct a numerical method based on Euler method accompanied with piecewise constant interpolation. The method is based on the idea of separating the current state and the prehistory function. The convergence of the method is stated and proved. Numerical experiments are given to clarify the good agreement between numerical and theoretical results. © 201

A NUMERICAL SOLUTION FOR A CLASS OF TIME FRACTIONAL DIFFUSION EQUATIONSWITH DELAY

This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4) in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results

Numerical Studies for Fractional Functional Differential Equations with Delay Based on BDF-Type Shifted Chebyshev Approximations

Fractional functional differential equations with delay (FDDEs) have recently played a significant role in modeling of many real areas of sciences such as physics, engineering, biology, medicine, and economics. FDDEs often cannot be solved analytically so the approximate and numerical methods should be adapted to solve these types of equations. In this paper we consider a new method of backward differentiation formula- (BDF-) type for solving FDDEs. This approach is based on the interval approximation of the true solution using the Clenshaw and Curtis formula that is based on the truncated shifted Chebyshev polynomials. It is shown that the new approach can be reformulated in an equivalent way as a Runge-Kutta method and the Butcher tableau of this method is given. Estimation of local and global truncating errors is deduced and this leads to the proof of the convergence for the proposed method. Illustrative examples of FDDEs are included to demonstrate the validity and applicability of the proposed approach

A Fractional Analog of Crank–Nicholson Method for the Two Sided Space Fractional Partial Equation with Functional Delay

For two sided space fractional diffusion equation with time functional after-effect, an implicit numerical method is constructed and the order of its convergence is obtained. The method is a fractional analogue of the Crank–Nicholson method, and also uses interpolation and extrapolation of the prehistory of model with respect to time.This work was supported by Government of the Russian Federation program 02.A03.21.0006on 27.08.2013 and by Russian Science Foundation 14-35-00005