Interannual Variation of Transpiration and Its Modeling of a Larch Plantation in Semiarid Northwest China

Quantifying the variation of forest transpiration (T) is important not only for understanding the water and energy budget of forest ecosystems but also for the prediction, evaluation, and management of hydrological effects as well as many other ecosystem services of forests under the changes of climate, vegetation, and anthropological impacts. The accurate prediction of T, a key component of water used by forests, requires mechanism-based models describing the T response to environmental and canopy conditions. The daily T of a larch (Larix principis-rupprechtti) plantation was measured through monitoring the sap flow in the growing season (from May to September) of a dry year (2010), a normal year (2012), and a wet year (2014) at a shady slope in the semi-arid area of Liupan Mountains in northwest China. Meanwhile, the meteorological conditions, soil moisture, and forest canopy leaf area index (LAI) were monitored. To get a simple and easily applicable T model, the numerous influencing parameters were grouped into three factors: the atmospheric evapotranspiration demand indicated by the potential evapotranspiration (PET), the soil water supply ability indicated by the relative extractable soil water content (REW), and the vegetation transpiration capacity indicated by the forest canopy LAI. The T model was established as a continuous multiplication of the T response equations to individual factors, which were determined using the upper boundary lines of measured data. The effect of each factor on the T in a dry year (2010) or normal year (2012) was assessed by comparing the measured T in the baseline of the wet year (2014) and the model predicted T, which was calculated through inputting the actual data of the factor (i.e., PET) to be assessed in the dry or normal year and the measured data of other two factors (i.e., REW, LAI) in the baseline of the wet year. The results showed that the mean daily T was 0.92, 1.05, and 1.02 mm; and the maximum daily T was 1.78, 1.92, and 1.89 mm in 2010, 2012, and 2014, respectively. The T response follows a parabolic equation to PET, but a saturated exponential equation to REW and LAI. The T model parameters were calibrated using measured data in 2010 and 2012 (R2 = 0.89, Nash coefficient = 0.88) and validated using measured data in 2014 satisfactorily (R2 = 0.89, Nash coefficient = 0.79). It showed a T limitation in the dry year 2010 for all factors (18.5 mm by PET, 11.5 mm by REW, and 17.8 mm by LAI); while a promotion for PET (1.4 mm) and a limitation for REW (4.2 mm) and LAI (14.3 mm) in the normal year 2012. The daily T model established in this study can be helpful to assess the individual factor impact on T and improve the daily T prediction under changing environmental and canopy conditions.

Orthogonal bases in a topological algebra are Schauder bases

In a topological algebra with separately continuous multiplication, the result quoted in the title is proved.

Footnote to a paper of Baker and Mines

Let S be a semigroup with a compact topology in which multiplication is continuous on the left (i.e. xi→x implies xiy→xy for each y in S). Then S has a minimal left ideal L which is compact; each idempotent e in L is a right identity for L (xe = xfor each x ∈ L)and L = Se; Ge = eL is a group and L is the union of all such groups; and if f is a second idempotent in L, the canonical map x ↦ fx of Ge to Gf is an algebraic isomorphism (see Ruppert(2) for these facts). Baker and Milnes(1), §4(A), have observed that, in the case in which S is the Stone–Cech compactification of a discrete abelian group, the canonical map from Ge to Gf may not be a homeomorphism. (This contrasts with the situation in compact semigroups with separately continuous multiplication.) We present a simple proof of a more definitive result.

Uniqueness of invariant means on certain introverted spaces

Let S be a topological semigroup with separately continuous multiplication and H a uniformly closed invariant subspace of LUC(S) (the space of left uniformly continuous bounded functions on S ) that contains the constants. It is shown that if H is left introverted and H admits a tight two-sided invariant mean m, then for each h ∈ H, m(h) is the unique constant function in the norm closed convex hull of the left orbit of h; consequently, H has a unique left invariant mean. (In fact, it is enough for H to admit a tight right invariant mean and a left invariant mean. ) For certain S, a similar result is obtained when H is a left compact-open introverted subspace of LCC(S) (the space of left compact-open continuous functions on S ).

Primitive idempotent measures on compact semigroups

Let S be a compact semigroup (with jointly continuous multiplication) and let P(S) denote the probability measures on S, i.e. the positive regular Borel measures on S with total mass one. Then P(S) is a compact semigroup with convolution multiplication and the weak* topology. Let II(P(S)) denote the set of primitive (or minimal) idempotents in P(S). Collins (2) and Pym (5) respectively have given complete descriptions of II(P(S)) when S is a group and when K(S), the kernel of S, is not a group. Choy (1) has given some characterizations of II(P(S)) for the general case. In this paper we present some detailed and intrinsic characterizations of II((P(S)) for various classes of compact semigroups that are not covered by the results of Collins and Pym.

Characteristics of five cell types appearing during in vitro culture of embryonic material from Drosophila melanogaster

Although attempts have been made over a number of decades to achieve successful tissue culture of Drosophila material, progress has been held back until recently by a lack of basic information on the chemical and physiological characteristics of the haemolymph of the organism necessary for a reasoned formulation of a culture medium. In 1963, Begg & Cruickshank published details of the mineral composition, osmotic pressure and pH of the haemolymph of third instar larvae, and this has provided the basis for a more satisfactory approach, as reflected in an increasing amount of fruitful work since reported. Much of this work has been done with embryonic material. Horikawa & Fox (1964) claimed continuous multiplication of a small type of early embryonic cell; Lesseps (1965) described re-aggregation of dissociated embryonic cells in culture, with possible development of muscle cells, nerve cells and oenocytes in the aggregates.

Compact semigroups in commutative Banach algebras

A monothetic semigroup is a topological semigroup with jointly continuous multiplication which contains a dense cyclic subsemigroup. These semi-groups arise in a natural way in the study of semi-algebras. In (4) we showed that a compact monothetic semigroup in a Banach algebra can be characterized in terms of the spectral properties of a generating element. In this paper these spectral theorems are linked with the well-known structure theory of compact semigroups.