Organic amendments and organic vegetable farming under plastic cover: Observations after six years of application

During an experiment carried out over a six-year period, annual applications of large quantities of two types of compost led to an increase in the carbon level in the ground but had little impact on its physicochemical characteristics. No significant effect was revealed on successive vegetable crops. In contrast, it was shown that these cropping systems had specific characteristics. Cropping conditions under plastic cover lead to a high level of mineralisation of the endogenous organic matter and a limited lixiviation of nutrients. As a result of frequent over-fertilisation practices in the past in conventional farming systems, deep soil horizons may contain large stocks of minerals, part of which will be tapped by crops over the years following a conversion to organic farming. In our experiment, this contribution of the soil to subsequent crop nutrient supply largely compensated for the reduction of inputs applied to summer crops up to the sixth year. We therefore hypothesize that these types of effects sustainably mask the impact of changes in fertilisation practices linked to the conversion to organic agriculture

On the domain wall partition functions of level-1 affine so(n) vertex models

We derive determinant expressions for domain wall partition functions of level-1 affine so(n) vertex models, n >= 4, at discrete values of the crossing parameter lambda = m pi / 2(n-3), m in Z, in the critical regime.Comment: 14 pages, 13 figures included in latex fil

Spin chains and combinatorics: twisted boundary conditions

The finite XXZ Heisenberg spin chain with twisted boundary conditions was considered. For the case of even number of sites $N$, anisotropy parameter -1/2 and twisting angle $2 \pi /3$ the Hamiltonian of the system possesses an eigenvalue $-3N/2$. The explicit form of the corresponding eigenvector was found for $N \le 12$. Conjecturing that this vector is the ground state of the system we made and verified several conjectures related to the norm of the ground state vector, its component with maximal absolute value and some correlation functions, which have combinatorial nature. In particular, the squared norm of the ground state vector is probably coincides with the number of half-turn symmetric alternating sign $N \times N$ matrices.Comment: LaTeX file, 7 page

SM(2,4k) fermionic characters and restricted jagged partitions

A derivation of the basis of states for the $SM(2,4k)$ superconformal minimal models is presented. It relies on a general hypothesis concerning the role of the null field of dimension $2k-1/2$. The basis is expressed solely in terms of $G_r$ modes and it takes the form of simple exclusion conditions (being thus a quasi-particle-type basis). Its elements are in correspondence with $(2k-1)$-restricted jagged partitions. The generating functions of the latter provide novel fermionic forms for the characters of the irreducible representations in both Ramond and Neveu-Schwarz sectors.Comment: 12 page

New Finite Rogers-Ramanujan Identities

We present two general finite extensions for each of the two Rogers-Ramanujan identities. Of these one can be derived directly from Watson's transformation formula by specialization or through Bailey's method, the second similar formula can be proved either by using the first formula and the q-Gosper algorithm, or through the so-called Bailey lattice.Comment: 19 pages. to appear in Ramanujan

Bethe roots and refined enumeration of alternating-sign matrices

The properties of the most probable ground state candidate for the XXZ spin chain with the anisotropy parameter equal to -1/2 and an odd number of sites is considered. Some linear combinations of the components of the considered state, divided by the maximal component, coincide with the elementary symmetric polynomials in the corresponding Bethe roots. It is proved that those polynomials are equal to the numbers providing the refined enumeration of the alternating-sign matrices of order M+1 divided by the total number of the alternating-sign matrices of order M, for the chain of length 2M+1.Comment: LaTeX 2e, 12 pages, minor corrections, references adde

Phase I multicenter study of combined high-dose ifosfamide and doxorubicin in the treatment of advanced sarcomas

Ifosfamide and doxorubicin are the most active agents in the treatment of sarcomas and are characterized by a marked dose-response relationship. The objective of this study was to determine the maximum tolerated dose (MTD) of both agents in combination under granulocyte-macrophage colony-stimulating factor (GM-CSF) cover. Patients and methods: Thirty-three patients with untreated sarcomas (soft tissue: n = 20; gynecological: n = 11; bone: n = 2) were treated with ifosfamide 12 g/m2 by continuous i.v. infusion over five days and doxorubicin with dose escalation from 50 mg/m2 i.v. bolus divided on two days, then to 60 mg/m2bolus divided on three days. Ifosfamide was reduced to 10 g/m2 and doxorubicin was further escalated up to 90 mg/m2. GM-CSF (5 μg/kg/day subcutaneously) was started 24 hours after chemotherapy and continued for 10 days. Results: The MTD was reached with the combination of ifosfamide at 12 g/m2 and doxorubicin at 60 mg/m2. But with ifosfamide 10 g/m2 and doxorubicin 90 mg/m2 the MTD was not obtained. While severe leukopenia and granulopenia were observed at all-dose levels, severe anemia was more frequently related to the highest dose of ifosfamide. Severe thrombopenia and mucositis were more commonly observed at the highest dose of doxorubicin. Ifosfamide 10 g/m2 and doxorubicin 90 mg/m2 induced WHO grade 4 leukopenia in 58%, grade 3-4 thrombopenia in 42%, and anemia in 31% of cycles. Mucositis was minor in 50% of cycles. The overall response rate among 31 evaluable patients was 55% (95 confidence interval (CI): 36%-73%), with four (13%) complete responders and 13 (42%) partial responders. Response rates based on soft-tissue sarcomas or gynecological sarcomas alone were similar. Ten patients could be treated by elective surgery and/or radiotherapy. The total group of patients reached a median survival of two years, with 25% (SE 8%) survivors after three years. Conclusions: The dose level of ifosfamide 10 g/m2 and doxorubicin 90 mg/m2 with supportive GM-CSF is manageable in a multicenter setting and should be further tested in regular phase II trials, including patients with gynecological and soft-tissue sarcomas. Transient toxicity with myelosup-pression should be accepted in order to obtain a high anti-tumor activity of this regimen and a potential improvement in surviva

The Razumov-Stroganov conjecture: Stochastic processes, loops and combinatorics

A fascinating conjectural connection between statistical mechanics and combinatorics has in the past five years led to the publication of a number of papers in various areas, including stochastic processes, solvable lattice models and supersymmetry. This connection, known as the Razumov-Stroganov conjecture, expresses eigenstates of physical systems in terms of objects known from combinatorics, which is the mathematical theory of counting. This note intends to explain this connection in light of the recent papers by Zinn-Justin and Di Francesco.Comment: 6 pages, 4 figures, JSTAT News & Perspective

Higher spin vertex models with domain wall boundary conditions

We derive determinant expressions for the partition functions of spin-k/2 vertex models on a finite square lattice with domain wall boundary conditions.Comment: 14 pages, 12 figures. Minor corrections. Version to appear in JSTA

Inverse problems associated with integrable equations of Camassa-Holm type; explicit formulas on the real axis, I

The inverse problem which arises in the Camassa--Holm equation is revisited for the class of discrete densities. The method of solution relies on the use of orthogonal polynomials. The explicit formulas are obtained directly from the analysis on the real axis without any additional transformation to a "string" type boundary value problem known from prior works