Production of pyrolytic oil from ULDP plastics using silica-alumina catalyst and used as fuel for DI diesel engine

A rapid increase in the use of non-biodegradable plastics and their disposal after use has had a detrimental impact on the environment. Used plastics (used low-density polyethylene – ULDP) were selected as feedstock for the extraction of pyrolytic oil. The pyrolysis process was carried out in a semi-batch reactor with a silica alumina catalyst in the existence of fluidizing gas N₂ in a reactor at 500 °C for 60 min. The maximum liquid, gas, and char yields were 93.5 wt%, 5.4 wt%, and 1.1 wt%, respectively. Experimental analysis was carried out to obtain their functional and structural groups by FT-IR and the carbon distribution was identified by GC-MS analysis. The blends of 20%, 40%, 60%, 80%, and 100% on a volume basis were chosen for the detailed study. For the pyrolytic blends, the combustion, performance, and emission characteristics were tested at different engine loads. During combustion, the heat release rate was extremely high for neat ULDP oil because of the high energy content and a higher cetane index. The efficiency of ULDP20 was higher than in other blends, whereas NOx and smoke emissions of ULDP20 were lower among the blends but higher than diesel. ULDP20 performed similarly as diesel. Hence, ULDP20 is recommended as a fuel for the diesel engine.

Lower acidity ratio of SA catalyst influences higher yield of ULDP oil and is suggested as a novel fuel for unmodified diesel engine.     

Riemann hypothesis for period polynomials of modular forms

The period polynomial r_f(z) for an even weight k ≥ 4 newform f ∈ S_k(Γ₀(N)) is the generating function for the critical values of L(f, s). It has a functional equation relating r_f(z) to rf(−1Nz). We prove the Riemann hypothesis for these polynomials: that the zeros of r_f(z) lie on the circle |z|=1/N. We prove that these zeros are equidistributed when either k or N is large.Let f ∈ S_k(Γ₀(N)) be a newform (1, 2) of even weight k and level N. Associated to f is its L-function L(f, s), which has been normalized so that the completed L-function,Λ(f,s):=(N2π)sΓ(s)L(f,s),satisfies the functional equation Λ(f, s) = ?(f)Λ(f, k ? s), with ?(f) = ±1. Recall that the completed L-function arises as a period integral of the newform f:Λ(f,s)=Ns/2∫0∞f(iy)ysdyy.[1.1]The focus of this paper is the period polynomial associated to f, the degree k ? 2 polynomialrf(z):=∫0i∞f(τ)(τ−z)k−2dτ.[1.2]Expanding (τ?z)^k?2, and using Eq. 1.1, we may also express the period polynomial byrf(z)=ik−1N−k−12 ∑n=0k−2 (k−2n)(Niz)nΛ(f,k−1−n),[1.3]or equivalently asrf(z)=−(k−2)!(2πi)k−1 ∑n=0k−2 (2πiz)nn!L(f,k−n−1).[1.4]In other words, r_f(z) is a generating function for the critical values L(f, 1), L(f, 2), …, L(f, k ? 1). For general facts on period polynomials, the reader is encouraged to see refs. 3–7; other papers broadly related to the themes of this paper are refs. 8 and 9.Using the functional equation Λ(f, s) = ?(f)Λ(f, k ? s) in Eq. 1.3, we find thatrf(z)=−ikϵ(f)(Nz)k−22rf(−1Nz),so that if ρ is a zero of r_f(z) then so is ?1/(Nρ). In analogy with the Riemann hypothesis, we may ask whether all of the zeros of r_f(z) lie on the circle |ρ|=1/N. For Hecke eigenforms on SL₂(?), this was recently established by El-Guindy and Raj (10), who showed that the zeros of r_f(z) (for N = 1) are all on the unit circle |z| = 1. Their work was inspired by the previous work by Conrey et al. (11), who proved an analogous result for odd period polynomials again for full level. We show that this “Riemann hypothesis” holds in general for all newforms of weight at least 4 and any level.

Theorem 1.1.

For any even integer k at least 4, and any level N, all of the zeros of the period polynomial r_f(z) are on the circle |z|=1/N.

Remark:

Period polynomials for weight 2 newforms f are constant multiples of L(f, 1).

Example 1:

The period polynomial for the normalized Hecke eigenform Δ(z) ∈ S₁₂(Γ₀(1)) isrΔ(z)=ωΔ+rΔ+(z)+ωΔ−rΔ−(z)≈0.114379i×(36691z10−z8+3z6−3z4+z2−36691) +0.00926927(4z9−25z7+42z5−25z3+4z).All 10 zeros of r_Δ(z) are on |z| = 1.

Example 2:

For the unique weight 4 newform f(z) = q ? 4q³ ? 2q⁵ +  ?  on Γ₀(8), we haveL(f, 1) ≈ 0.3545006…, ???L(f, 2) ≈ 0.6900311…, ???L(f, 3) ≈ 0.8746953…, which in turn implies that r_f(z) ≈ 0.0564205361iz² + 0.0349573870z ? 0.00705256701815496i. The roots are  ≈ ±0.17037672 + 0.30979311i, and their norms are ≈1/(22).

Remark:

Manin (12) has used the work of Conrey et al. (11) to construct zeta functions that satisfy the Riemann hypothesis. He suggests that these polynomials arise from non-Tate motives and geometric objects lying below Spec?Z but not over F₁. Using the P_f(z) defined below, one obtains further such polynomials mutatis mutandis.If the weight or level is large enough, then the zeros of r_f are regularly spaced on the circle |z|=1/N. To state this conveniently, and for our later work, we shall put m: = (k ? 2)/2 throughout and definePf(z)=12(2mm)Λ(f,k2)+∑j=1m(2mm+j)Λ(f,k2+j)zj.[1.5]Then, using the functional equation, we see thatrf(ziN)=ik−1N−k−12ϵ(f)zm(Pf(z)+ϵ(f)Pf(1z)).[1.6]Therefore, to understand the zeros of r_f, it is enough to understand the zeros of P_f(z) + ?(f)P_f(1/z), and Theorem 1.1 states that this function has all its zeros on the unit circle |z| = 1. If we restrict to the unit circle |z| = 1, then P_f(z) + ?(f)P_f(1/z) is either a trigonometric cosine or a trigonometric sine polynomial [depending on whether ?(f) equals 1 or ?1], and our proof of Theorem 1.1 proceeds by finding the right number of sign changes as z varies over the unit circle. If k or N is large enough, the proof allows us to establish the following result on the location of the roots.

Theorem 1.2.

The following are true.

• i)Suppose that k = 4. If ?(f) = ?1, then the zeros of r_f(z) are ±i/N. If ?(f) = 1 and N is sufficiently large, then the zeros of r_f(z) are located at ±(1+O(N−14+ϵ))/N.
• ii)If k ≥ 6 and either N or k is large enough, then the roots of r_f(z) may be written as

1iNexp(iθℓ+O(12kN)),

• where for 0 ≤ ? ≤ 2m ? 1 we denote by θ_? the unique solution in [0,2π) to the equation

m θℓ−2πNsin θℓ={π2+ℓπif ϵ(f)=1ℓπif ϵ(f)=−1.Our arguments readily allow us to quantify the results in Theorem 1.2. For example, the arguments in section 6 give that in part ii above, the implied O-constant may be taken as 10⁹, although this is a gross overestimate. The arguments in section 5 locate sign changes even if the values of k or N are only moderately large.Suppose that ?(f) = 1. By counting sign changes, one consequence of Theorem 1.1 is that P_f(?1) has sign (?1)^m. In other words, if ?(f) = 1, then we must have12(2mm)(−1)mΛ(f,k2)+∑j=0m−1(−1)j(2m2m−j)Λ(f,k−1−j)>0.[1.7]For any weight k, this inequality is clear for large enough N because the term j = 0 above dominates all other terms. However, it is interesting that such an inequality holds for all small weights and small level as well, and we wonder whether it has any other significance. In section 4 we give a proof of this inequality in the weight 6 case based on the Hadamard factorization formula. We also give there a more illuminating proof of this inequality based on the Riemann hypothesis for Λ(f, s).     

CD8+ T cells inhibit metastasis and CXCL4 regulates its function

Background The mechanism by which immune cells regulate metastasis is unclear. Understanding the role of immune cells in metastasis will guide the development of treatments improving patient survival.Methods We used syngeneic orthotopic mouse tumour models (wild-type, NOD/scid and Nude), employed knockout (CD8 and CD4) models and administered CXCL4. Tumours and lungs were analysed for cancer cells by bioluminescence, and circulating tumour cells were isolated from blood. Immunohistochemistry on the mouse tumours was performed to confirm cell type, and on a tissue microarray with 180 TNBCs for human relevance. TCGA data from over 10,000 patients were analysed as well.Results We reveal that intratumoral immune infiltration differs between metastatic and non-metastatic tumours. The non-metastatic tumours harbour high levels of CD8⁺ T cells and low levels of platelets, which is reverse in metastatic tumours. During tumour progression, platelets and CXCL4 induce differentiation of monocytes into myeloid-derived suppressor cells (MDSCs), which inhibit CD8⁺ T-cell function. TCGA pan-cancer data confirmed that CD8^lowPlatelet^high patients have a significantly lower survival probability compared to CD8^highPlatelet^low.Conclusions CD8⁺ T cells inhibit metastasis. When the balance between CD8⁺ T cells and platelets is disrupted, platelets produce CXCL4, which induces MDSCs thereby inhibiting the CD8⁺ T-cell function.Subject terms: Tumour immunology, Metastasis     

UDP glucuronosyltransferase (UGT) 1A6 pharmacogenetics: II. Functional impact of the three most common nonsynonymous UGT1A6 polymorphisms (S7A, T181A, and R184S)

The objective of this study was to use recombinant enzymes and human liver microsomes (HLMs) to comprehensively evaluate the functional impact of the three most common nonsynonymous polymorphisms (S7A, T181A, and R184S) identified in the human UDP glucuronosyltransferase (UGT) 1A6 gene. In addition to the known allozymes, other possible amino acid variants were expressed in human embryonic kidney (HEK)293 cells to enable structure-function analysis. Initial studies using different substrates (serotonin, 5-hydroxytryptophol, 4-nitrophenol, acetaminophen, and valproic acid) showed similar results with 2-fold higher glucuronidation by UGT1A6(*)2 (S7A/T181A/R184S) compared with UGT1A6(*)1 (reference), and intermediate activities for other variants. Enzyme kinetic analyses with the UGT1A6-specific substrate (serotonin) showed 50% lower K(m) values for all R184S variants and 2-fold higher V(max) values for both S7A/T181A variants compared with UGT1A6(*)1. Furthermore, intrinsic clearance (V(max)/K(m)) values were highest for the UGT1A6(*)2 allozyme (2.3-fold over UGT1A6(*)1), resulting from additive effects of higher enzyme affinity and activity. As expected, K(m) values of (*)1/(*)1 genotyped HLMs (5.4 +/- 0.2 mM) were similar to recombinant UGT1A6(*)1 (5.8 +/- 0.6 mM). Conversely, (*)2/(*)2 HLMs showed higher K(m) values (7.0 +/- 0.3 mM) rather than the lower K(m) values displayed by recombinant UGT1A6(*)2 (3.6 +/- 0.3 mM), suggesting that this allozyme may display different enzyme kinetic behavior in HLMs compared with HEK293 cells. At best, these polymorphisms were predicted to account for 15 to 20% of the observed 13-fold variability in glucuronidation of UGT1A6 substrates by HLMs, indicating that there are likely other genetic or environmental factors responsible for the majority of this variation.